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Journal articles on the topic 'Ideal sheaves'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Guan, Qi’an, Zhenqian Li, and Xiangyu Zhou. "Stability of Multiplier Ideal Sheaves." Chinese Annals of Mathematics, Series B 43, no. 5 (September 2022): 819–32. http://dx.doi.org/10.1007/s11401-022-0360-3.

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2

Cutkosky, Steven Dale, Lawrence Ein, and Robert Lazarsfeld. "Positivity and complexity of ideal sheaves." Mathematische Annalen 321, no. 2 (October 1, 2001): 213–34. http://dx.doi.org/10.1007/s002080100220.

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3

WESSLER, MARKUS. "MULTIPLIER IDEAL SHEAVES ON FIBRED PRODUCTS OF CERTAIN SINGULAR VARIETIES." International Journal of Mathematics 17, no. 04 (April 2006): 393–99. http://dx.doi.org/10.1142/s0129167x0600359x.

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In [3], we discussed the compatibility of multiplier ideal sheaves with fibred products. Multiplier ideal sheaves on singular varieties generalize in a natural way the ℚ-divisors on nonsingular varieties. However, there was one central result in [3] which we proved only for nonsingular varieties. In this paper we extend this to a certain class of singular varieties.

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4

Fujino, Osamu. "Theory of non-lc ideal sheaves: Basic properties." Kyoto Journal of Mathematics 50, no. 2 (2010): 225–45. http://dx.doi.org/10.1215/0023608x-2009-011.

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5

Popovici, Dan. "Effective local finite generation of multiplier ideal sheaves." Annales de l’institut Fourier 60, no. 5 (2010): 1561–94. http://dx.doi.org/10.5802/aif.2565.

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6

Phong, D. H., Natasa Sesum, and Jacob Sturm. "Multiplier ideal sheaves and the Kähler-Ricci flow." Communications in Analysis and Geometry 15, no. 3 (2007): 613–32. http://dx.doi.org/10.4310/cag.2007.v15.n3.a7.

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7

Niu, Wenbo. "Some results on asymptotic regularity of ideal sheaves." Journal of Algebra 377 (March 2013): 157–72. http://dx.doi.org/10.1016/j.jalgebra.2012.11.042.

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8

Guenancia, Henri. "Toric plurisubharmonic functions and analytic adjoint ideal sheaves." Mathematische Zeitschrift 271, no. 3-4 (June 4, 2011): 1011–35. http://dx.doi.org/10.1007/s00209-011-0900-0.

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9

Siu, Yum-Tong. "Multiplier ideal sheaves in complex and algebraic geometry." Science in China Series A: Mathematics 48, S1 (December 2005): 1–31. http://dx.doi.org/10.1007/bf02884693.

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10

WESSLER, MARKUS. "A SHORT NOTE ON MULTIPLIER IDEAL SHEAVES ON SINGULAR VARIETIES." International Journal of Mathematics 14, no. 04 (June 2003): 361–69. http://dx.doi.org/10.1142/s0129167x03001855.

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11

Larusson, Finnur, and Ragnar Sigurdsson. "Plurisubharmonic extremal functions, Lelong numbers and coherent ideal sheaves." Indiana University Mathematics Journal 48, no. 4 (1999): 0. http://dx.doi.org/10.1512/iumj.1999.48.1767.

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12

Fujino, Osamu, and Shin-ichi Matsumura. "Injectivity theorem for pseudo-effective line bundles and its applications." Transactions of the American Mathematical Society, Series B 8, no. 27 (October 13, 2021): 849–84. http://dx.doi.org/10.1090/btran/86.

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We formulate and establish a generalization of Kollár’s injectivity theorem for adjoint bundles twisted by suitable multiplier ideal sheaves. As applications, we generalize Kollár’s torsion-freeness, Kollár’s vanishing theorem, and a generic vanishing theorem for pseudo-effective line bundles. Our approach is not Hodge theoretic but analytic, which enables us to treat singular Hermitian metrics with nonalgebraic singularities. For the proof of the main injectivity theorem, we use L 2 L^{2} -harmonic forms on noncompact Kähler manifolds. For applications, we prove a Bertini-type theorem on the restriction of multiplier ideal sheaves to general members of free linear systems.

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13

Scalise, Jacopo Vittorio. "Framed symplectic sheaves on surfaces." International Journal of Mathematics 29, no. 01 (January 2018): 1850007. http://dx.doi.org/10.1142/s0129167x18500076.

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A framed symplectic sheaf on a smooth projective surface [Formula: see text] is a torsion-free sheaf [Formula: see text] together with a trivialization on a divisor [Formula: see text] and a morphism [Formula: see text] satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for [Formula: see text]. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

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14

Guan, Qi’an, and Xiangyu Zhou. "Restriction formula and subadditivity property related to multiplier ideal sheaves." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 769 (December 1, 2020): 1–33. http://dx.doi.org/10.1515/crelle-2019-0043.

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AbstractWe give a restriction formula on jumping numbers which is a reformulation of Demailly–Ein–Lazarsfeld’s important restriction formula for multiplier ideal sheaves and a generalization of Demailly–Kollár’s important restriction formula on complex singularity exponents, and then we establish necessary conditions for the extremal case in the reformulated formula; we pose the subadditivity property on the complex singularity exponents of plurisubharmonic functions which is a generalization of Demailly–Kollár’s fundamental subadditivity property, and then we establish necessary conditions for the extremal case in the generalization. We also obtain two sharp relations on jumping numbers, introduce a new invariant of plurisubharmonic singularities and get its decreasing property for consecutive differences.

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15

Futaki, Akito, and Yuji Sano. "Multiplier ideal sheaves and integral invariants on toric Fano manifolds." Mathematische Annalen 350, no. 2 (August 15, 2010): 245–67. http://dx.doi.org/10.1007/s00208-010-0556-9.

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16

Zhou, Xiangyu, and Langfeng Zhu. "Extension of cohomology classes and holomorphic sections defined on subvarieties." Journal of Algebraic Geometry 31, no. 1 (September 6, 2021): 137–79. http://dx.doi.org/10.1090/jag/766.

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In this paper, we obtain two extension theorems for cohomology classes and holomorphic sections defined on analytic subvarieties, which are defined as the supports of the quotient sheaves of multiplier ideal sheaves of quasi-plurisubharmonic functions with arbitrary singularities. The first result gives a positive answer to a question posed by Cao-Demailly-Matsumura and unifies a few well-known injectivity theorems. The second result generalizes and optimizes a general L 2 L^2 extension theorem obtained by Demailly.

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17

Chen, Huachen. "O’Grady’s birational maps and strange duality via wall-hitting." International Journal of Mathematics 30, no. 09 (August 2019): 1950044. http://dx.doi.org/10.1142/s0129167x19500447.

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We prove that O’Grady’s birational maps [K. G O’Grady, The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface, J. Algebr. Geom. 6(4) (1997) 599–644] between moduli of sheaves on an elliptic K3 surface can be interpreted as intermediate wall-crossing (wall-hitting) transformations at so-called totally semistable walls, studied by Bayer and Macrì [A. Bayer and E. Macrì, MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations, Inventiones Mathematicae 198(3) (2014) 505–590]. As a key ingredient, we describe the first totally semistable wall for ideal sheaves of [Formula: see text] points on the elliptic [Formula: see text]. As an application, we give new examples of strange duality isomorphisms, based on a result of Marian and Oprea [A. Marian and D. Oprea, Generic strange duality for K3 surfaces, with an appendix by Kota Yoshioka, Duke Math. J. 162(8) (2013) 1463–1501].

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18

Nadel, Alan Michael. "Multiplier Ideal Sheaves and Kahler-Einstein Metrics of Positive Scalar Curvature." Annals of Mathematics 132, no. 3 (November 1990): 549. http://dx.doi.org/10.2307/1971429.

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19

Larusson, Finnur, and Ragnar Sigurdsson. "Erratum to 'Plurisubharmonic extremal functions, Lelong numbers and coherent ideal sheaves'." Indiana University Mathematics Journal 50, no. 4 (2001): 1705–6. http://dx.doi.org/10.1512/iumj.2001.50.2279.

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20

Guan, Qi’An, and XiangYu Zhou. "Strong openness of multiplier ideal sheaves and optimal L 2 extension." Science China Mathematics 60, no. 6 (April 25, 2017): 967–76. http://dx.doi.org/10.1007/s11425-017-9055-5.

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21

Guan, Qi'an, and Xiangyu Zhou. "Characterization of multiplier ideal sheaves with weights of Lelong number one." Advances in Mathematics 285 (November 2015): 1688–705. http://dx.doi.org/10.1016/j.aim.2015.08.002.

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22

Guan, Qi'an, and Zhenqian Li. "Multiplier ideal sheaves associated with weights of log canonical threshold one." Advances in Mathematics 302 (October 2016): 40–47. http://dx.doi.org/10.1016/j.aim.2016.07.012.

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23

Katz, Sheldon, Wei-Ping Li, and Zhenbo Qin. "On certain moduli spaces of ideal sheaves and Donaldson-Thomas invariants." Mathematical Research Letters 14, no. 3 (2007): 403–11. http://dx.doi.org/10.4310/mrl.2007.v14.n3.a5.

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24

Niu, Wenbo. "A vanishing theorem and asymptotic regularity of powers of ideal sheaves." Journal of Algebra 344, no. 1 (October 2011): 246–59. http://dx.doi.org/10.1016/j.jalgebra.2011.06.035.

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25

Wu, Xiaojun. "On the hard Lefschetz theorem for pseudoeffective line bundles." International Journal of Mathematics 32, no. 06 (April 10, 2021): 2150035. http://dx.doi.org/10.1142/s0129167x2150035x.

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In this paper, we obtain a number of results related to the hard Lefschetz theorem for pseudoeffective line bundles, due to Demailly, Peternell and Schneider. Our first result states that the holomorphic sections produced by the theorem are in fact parallel, when the Chern connection associated with the singular metric is computed in the sense of currents, and the corresponding multiplier ideal sheaves are taken into account. Our proof is based on a control of the covariant derivative in the delicate approximation process used in the construction of these sections. Then we show that there is an isomorphism between the space of such parallel sections and the sheaf cohomology group of appropriate degree. As an application, we show that the closedness property of the sections produces a singular holomorphic foliation on the tangent bundle. Finally, we discuss some questions related to the optimality of the multiplier ideal sheaves involved in the generalized hard Lefschetz theorem.

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26

Shang, Shijie. "A remark on the Castelnuovo-Mumford regularity of powers of ideal sheaves." Journal of Pure and Applied Algebra 226, no. 12 (December 2022): 107143. http://dx.doi.org/10.1016/j.jpaa.2022.107143.

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27

de Fernex, Tommaso, and Christopher D. Hacon. "Singularities on normal varieties." Compositio Mathematica 145, no. 2 (March 2009): 393–414. http://dx.doi.org/10.1112/s0010437x09003996.

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AbstractIn this paper we generalize the definitions of singularities of pairs and multiplier ideal sheaves to pairs on arbitrary normal varieties, without any assumption on the variety being ℚ-Gorenstein or the pair being log ℚ-Gorenstein. The main features of the theory extend to this setting in a natural way.

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28

Matsumura, Shin-ichi. "An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities." Journal of Algebraic Geometry 27, no. 2 (August 17, 2017): 305–37. http://dx.doi.org/10.1090/jag/687.

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29

Nadel, A. M. "Multiplier ideal sheaves and existence of Kahler-Einstein metrics of positive scalar curvature." Proceedings of the National Academy of Sciences 86, no. 19 (October 1, 1989): 7299–300. http://dx.doi.org/10.1073/pnas.86.19.7299.

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30

Heier, Gordon. "Existence of Kähler–Einstein metrics and multiplier ideal sheaves on del Pezzo surfaces." Mathematische Zeitschrift 264, no. 4 (February 19, 2009): 727–43. http://dx.doi.org/10.1007/s00209-009-0486-y.

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31

Heier, Gordon. "Convergence of the Kähler-Ricci flow and multiplier ideal sheaves on del Pezzo surfaces." Michigan Mathematical Journal 58, no. 2 (August 2009): 423–40. http://dx.doi.org/10.1307/mmj/1250169070.

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32

Weinkove, Ben. "A complex Frobenius theorem, multiplier ideal sheaves and Hermitian-Einstein metrics on stable bundles." Transactions of the American Mathematical Society 359, no. 04 (October 16, 2006): 1577–93. http://dx.doi.org/10.1090/s0002-9947-06-03985-7.

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33

Brun, Morten, and Tim Römer. "On algebras associated to partially ordered sets." MATHEMATICA SCANDINAVICA 103, no. 2 (December 1, 2008): 169. http://dx.doi.org/10.7146/math.scand.a-15076.

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We continue the work [2] on sheaves of rings on finite posets. We present examples where the ring of global sections coincide with toric faces rings, quotients of a polynomial ring by a monomial ideal and algebras with straightening laws. We prove a rank-selection theorem which generalizes the well-known rank-selection theorem of Stanley-Reisner rings. Finally, we determine an explicit presentation of certain global rings of sections.

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34

Sano, Yuji. "Multiplier ideal sheaves and the Kähler–Ricci flow on toric Fano manifolds with large symmetry." Communications in Analysis and Geometry 20, no. 2 (2012): 341–68. http://dx.doi.org/10.4310/cag.2012.v20.n2.a5.

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35

Rubinstein, Yanir A. "On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow." Transactions of the American Mathematical Society 361, no. 11 (May 7, 2009): 5839–50. http://dx.doi.org/10.1090/s0002-9947-09-04675-3.

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36

Ahmadian, Razieh. "A principalization algorithm for locally monomial ideal sheaves on 3-folds with an application to toroidalization." Journal of Algebra 454 (May 2016): 139–80. http://dx.doi.org/10.1016/j.jalgebra.2016.01.031.

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37

Zhou, Xiangyu, and Langfeng Zhu. "Subadditivity of generalized Kodaira dimensions and extension theorems." International Journal of Mathematics 31, no. 12 (September 30, 2020): 2050098. http://dx.doi.org/10.1142/s0129167x20500986.

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In this paper, we introduce the notion of generalized Kodaira dimension with multiplier ideal sheaves, and prove the subadditivity of these generalized Kodaira dimensions for certain Kähler fibrations, which was originally obtained for Kodaira dimensions of algebraic fiber spaces by Kawamata and Viehweg. Our method is analytic and based on some new results in recent years. The crucial step in our proof is to prove an [Formula: see text] extension theorem for twisted pluricanonical sections on compact Kähler manifolds. Moreover, we also discuss the relation between two previous optimal [Formula: see text] extension theorems with singular weights on weakly pseudoconvex Kähler manifolds.

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38

Jeralds, Samuel, and Shrawan Kumar. "Root components for tensor product of affine Kac-Moody Lie algebra modules." Representation Theory of the American Mathematical Society 26, no. 27 (July 26, 2022): 825–58. http://dx.doi.org/10.1090/ert/617.

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Let g \mathfrak {g} be an affine Kac-Moody Lie algebra and let λ , μ \lambda , \mu be two dominant integral weights for g \mathfrak {g} . We prove that under some mild restriction, for any positive root β \beta , V ( λ ) ⊗ V ( μ ) V(\lambda )\otimes V(\mu ) contains V ( λ + μ − β ) V(\lambda +\mu -\beta ) as a component, where V ( λ ) V(\lambda ) denotes the integrable highest weight (irreducible) g \mathfrak {g} -module with highest weight λ \lambda . This extends the corresponding result by Kumar from the case of finite dimensional semisimple Lie algebras to the affine Kac-Moody Lie algebras. One crucial ingredient in the proof is the action of Virasoro algebra via the Goddard-Kent-Olive construction on the tensor product V ( λ ) ⊗ V ( μ ) V(\lambda )\otimes V(\mu ) . Then, we prove the corresponding geometric results including the higher cohomology vanishing on the G \mathcal {G} -Schubert varieties in the product partial flag variety G / P × G / P \mathcal {G}/\mathcal {P}\times \mathcal {G}/\mathcal {P} with coefficients in certain sheaves coming from the ideal sheaves of G \mathcal {G} -sub-Schubert varieties. This allows us to prove the surjectivity of the Gaussian map.

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39

ALUFFI, PAOLO. "Chern classes of blow-ups." Mathematical Proceedings of the Cambridge Philosophical Society 148, no. 2 (August 4, 2009): 227–42. http://dx.doi.org/10.1017/s0305004109990247.

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AbstractWe extend the classical formula of Porteous for blowing-up Chern classes to the case of blow-ups of possibly singular varieties along regularly embedded centers. The proof of this generalization is perhaps conceptually simpler than the standard argument for the nonsingular case, involving Riemann–Roch without denominators. The new approach relies on the explicit computation of an ideal, and a mild generalization of a well-known formula for the normal bundle of a proper transform ([8, B·6·10]).We also discuss alternative, very short proofs of the standard formula in some cases: an approach relying on the theory of Chern–Schwartz–MacPherson classes (working in characteristic 0), and an argument reducing the formula to a straightforward computation of Chern classes for sheaves of differential 1-forms with logarithmic poles (when the center of the blow-up is a complete intersection).

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40

Das, Sourav, Saurabh Kundu, and Arunansu Haldar. "Development of Continuously Cooled High Strength Bainitic Steel through Microstructural Engineering at Tata Steel." Materials Science Forum 702-703 (December 2011): 939–42. http://dx.doi.org/10.4028/www.scientific.net/msf.702-703.939.

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Bainitic steels, which are transformed at very low temperatures, offer an excellent combination of strength and ductility where the strength comes from the nano-structured bainitic plates and thin-film of austenite sandwiched between two bainite sheaves offers the ductility. The main drawback of this structure is the long transformation time which is not ideal for industrial application. Through the microstructural engineering, the extent and kinetics of transformation can be manipulated by judicious selection of alloy composition and process variables. The main challenge is to delay the transformation till the coiling stage and allow the formation of bainite only during the cooling of the coil. In the current work, an approach will be shown, starting from the alloy design based on thermodynamics till the cooling after coiling, which can satisfy the requirements to develop such steel with 1300 MPa UTS combined with 20% elongation (min).

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41

Darvas, Tamás, Eleonora Di Nezza, and Chinh H. Lu. "On the singularity type of full mass currents in big cohomology classes." Compositio Mathematica 154, no. 2 (November 9, 2017): 380–409. http://dx.doi.org/10.1112/s0010437x1700759x.

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Let $X$ be a compact Kähler manifold and $\{\unicode[STIX]{x1D703}\}$ be a big cohomology class. We prove several results about the singularity type of full mass currents, answering a number of open questions in the field. First, we show that the Lelong numbers and multiplier ideal sheaves of $\unicode[STIX]{x1D703}$-plurisubharmonic functions with full mass are the same as those of a current with minimal singularities. Second, given another big and nef class $\{\unicode[STIX]{x1D702}\}$, we show the inclusion ${\mathcal{E}}(X,\unicode[STIX]{x1D702})\cap \operatorname{PSH}(X,\unicode[STIX]{x1D703})\subset {\mathcal{E}}(X,\unicode[STIX]{x1D703})$. Third, we characterize big classes whose full mass currents are ‘additive’. Our techniques make use of a characterization of full mass currents in terms of the envelope of their singularity type. As an essential ingredient we also develop the theory of weak geodesics in big cohomology classes. Numerous applications of our results to complex geometry are also given.

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42

Chen, Jianke. "Generalized Canonical Isomorphisms on Determinant." Algebra Colloquium 23, no. 02 (March 16, 2016): 239–42. http://dx.doi.org/10.1142/s1005386716000262.

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In this paper we define tensor modules (sheaves) of Schur type and of generalized Schur type associated with given modules (sheaves), using the so-called Schur functors. According to the functorial property, we give a series of tensor modules (sheaves) of Schur types in a categorical description. The main conclusion is that, by using basic ideas of algebraic geometry, there exists a canonical isomorphism of different tensor modules (sheaves) of Schur types if the original sheaf is locally free, which is in fact a generalization of results in linear algebra into locally free sheaves.

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43

Nicoara, Andreea C. "Coherence and other properties of sheaves in the Kohn algorithm." International Journal of Mathematics 25, no. 08 (July 2014): 1450077. http://dx.doi.org/10.1142/s0129167x14500773.

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In the smooth case, we prove quasi-flasqueness for the sheaves of all subelliptic multipliers as well as at each of the steps of the Kohn algorithm on a pseudoconvex domain in ℂn. We use techniques by Jean-Claude Tougeron to show that if the domain has a real-analytic defining function, the modified Kohn algorithm involving generating ideals and taking real radicals only in the ring of real-analytic germs yields quasi-coherent sheaves. This sharpens a result obtained by J. J. Kohn in 1979.

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44

Nobile, Augusto, and Orlando E. Villamayor. "Zariski factorization theory for sheaves of ideals on arithmetic three-folds." Communications in Algebra 26, no. 8 (January 1998): 2669–88. http://dx.doi.org/10.1080/00927879808826303.

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45

Ben-Zvi, David, and Thomas Nevins. "Perverse bundles and Calogero–Moser spaces." Compositio Mathematica 144, no. 6 (November 2008): 1403–28. http://dx.doi.org/10.1112/s0010437x0800359x.

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AbstractWe present a simple description of moduli spaces of torsion-free 𝒟-modules (𝒟-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with Calogero–Moser quiver varieties. Namely, we show that the moduli of 𝒟-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T*X[n] in the rank-one case). The proof is based on the description of the derived category of 𝒟-modules on X by a noncommutative version of the Beilinson transform on P1.

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46

Wolpert, Scott A. "Products of twists, geodesic lengths and Thurston shears." Compositio Mathematica 151, no. 2 (October 9, 2014): 313–50. http://dx.doi.org/10.1112/s0010437x1400757x.

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AbstractThurston introduced shear deformations (cataclysms) on geodesic laminations–deformations including left and right displacements along geodesics. For hyperbolic surfaces with cusps, we consider shear deformations on disjoint unions of ideal geodesics. The length of a balanced weighted sum of ideal geodesics is defined and the Weil–Petersson (WP) duality of shears and the defined length is established. The Poisson bracket of a pair of balanced weight systems on a set of disjoint ideal geodesics is given in terms of an elementary$2$-form. The symplectic geometry of balanced weight systems on ideal geodesics is developed. Equality of the Fock shear coordinate algebra and the WP Poisson algebra is established. The formula for the WP Riemannian pairing of shears is also presented.

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47

Beklemishev, A. D. "Nonlinear saturation of ideal interchange modes in a sheared magnetic field." Physics of Fluids B: Plasma Physics 3, no. 6 (June 1991): 1425–37. http://dx.doi.org/10.1063/1.859708.

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48

PIRASHVILI, ILIA. "Topos points of quasi-coherent sheaves over monoid schemes." Mathematical Proceedings of the Cambridge Philosophical Society 169, no. 1 (March 11, 2019): 31–74. http://dx.doi.org/10.1017/s0305004119000069.

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AbstractLet X be a monoid scheme. We will show that the stalk at any point of X defines a point of the topos of quasi-coherent sheaves over X. As it turns out, every topos point of is of this form if X satisfies some finiteness conditions. In particular, it suffices for M/M× to be finitely generated when X is affine, where M× is the group of invertible elements.This allows us to prove that two quasi-projective monoid schemes X and Y are isomorphic if and only if and are equivalent.The finiteness conditions are essential, as one can already conclude by the work of A. Connes and C. Consani [3]. We will study the topos points of free commutative monoids and show that already for ℕ∞, there are ‘hidden’ points. That is to say, there are topos points which are not coming from prime ideals. This observation reveals that there might be a more interesting ‘geometry of monoids’.

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49

van Hoven, G., L. Sparks, and T. Tachi. "Ideal condensations due to perpendicular thermal conduction in a sheared magnetic field." Astrophysical Journal 300 (January 1986): 249. http://dx.doi.org/10.1086/163799.

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50

Nührenberg, C. "Ideal magnetohydrodynamic stability in stellarators with subsonic equilibrium flow." Plasma Physics and Controlled Fusion 63, no. 12 (November 17, 2021): 125035. http://dx.doi.org/10.1088/1361-6587/ac35ef.

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Abstract The effect of a subsonic flow, inherent to most stellarators because of a radial electric field, on their ideal magnetohydrodynamic (MHD) stability properties is studied employing the quasi-Lagrangian picture developed by Frieman and Rotenberg (1960 Rev. Mod. Phys. 32 898). The Mach number of the perpendicular E × B flow in stellarators is of order 0.01 and, therefore, admits the usage of a subsonic approximation in form of a static equilibrium. A mathematical formulation of the weak form of the stability equation with flow has been implemented in the ideal-MHD stability code CAS3D. This formulation uses magnetic coordinates and does not involve any derivatives across magnetic surfaces. In addition to the expected Doppler shift of frequencies, properties of the spectrum of the ideal MHD force operator, which are already known for tokamaks, but now also shown in the stellarator case, are: firstly, the appearance of unstable flow-induced continua stemming from the coupling of sound and Alfvén continuum branches with equal mode numbers; and, secondly, the existence of flow-induced, global, stable modes near extrema of sound continuum branches, the extrema, in turn, being generated by the influence of a sheared flow on the static sound continua.

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