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Journal articles on the topic 'K3 surfaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 October 2024

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1

Garbagnati, Alice. "On K3 Surface Quotients of K3 or Abelian Surfaces." Canadian Journal of Mathematics 69, no. 02 (April 2017): 338–72. http://dx.doi.org/10.4153/cjm-2015-058-1.

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Abstract The aim of this paper is to prove that a K3 surface is the minimal model of the quotient of an Abelian surface by a group G (respectively of a K3 surface by an Abelian group G) if and only if a certain lattice is primitively embedded in its Néron-Severi group. This allows one to describe the coarse moduli space of the K3 surfaces that are (rationally) G-covered by Abelian or K3 surfaces (in the latter case G is an Abelian group). When G has order 2 or G is cyclic and acts on an Abelian surface, this result is already known; we extend it to the other cases. Moreover, we prove that a K3 surface XG is the minimal model of the quotient of an Abelian surface by a group G if and only if a certain configuration of rational curves is present on XG . Again, this result was known only in some special cases, in particular, if G has order 2 or 3.

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2

Kim, Hoil, and Chang-Yeong Lee. "Noncommutative K3 surfaces." Physics Letters B 536, no. 1-2 (May 2002): 154–60. http://dx.doi.org/10.1016/s0370-2693(02)01807-5.

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3

Katsura, Toshiyuki, and Matthias Schütt. "Zariski K3 surfaces." Revista Matemática Iberoamericana 36, no. 3 (November 11, 2019): 869–94. http://dx.doi.org/10.4171/rmi/1152.

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4

Keum, Jong Hae. "Every algebraic Kummer surface is the K3-cover of an Enriques surface." Nagoya Mathematical Journal 118 (June 1990): 99–110. http://dx.doi.org/10.1017/s0027763000003019.

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A Kummer surface is the minimal desingularization of the surface T/i, where T is a complex torus of dimension 2 and i the involution automorphism on T. T is an abelian surface if and only if its associated Kummer surface is algebraic. Kummer surfaces are among classical examples of K3-surfaces (which are simply-connected smooth surfaces with a nowhere-vanishing holomorphic 2-form), and play a crucial role in the theory of K3-surfaces. In a sense, all Kummer surfaces (resp. algebraic Kummer surfaces) form a 4 (resp. 3)-dimensional subset in the 20 (resp. 19)-dimensional family of K3-surfaces (resp. algebraic K3 surfaces).

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5

Hayashi, Taro. "Double cover K3 surfaces of Hirzebruch surfaces." Advances in Geometry 21, no. 2 (April 1, 2021): 221–25. http://dx.doi.org/10.1515/advgeom-2020-0034.

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Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

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6

Artebani, Michela, Jürgen Hausen, and Antonio Laface. "On Cox rings of K3 surfaces." Compositio Mathematica 146, no. 4 (March 25, 2010): 964–98. http://dx.doi.org/10.1112/s0010437x09004576.

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AbstractWe study Cox rings of K3 surfaces. A first result is that a K3 surface has a finitely generated Cox ring if and only if its effective cone is rational polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3 surfaces of Picard number two, and explicitly compute the Cox rings of generic K3 surfaces with a non-symplectic involution that have Picard number 2 to 5 or occur as double covers of del Pezzo surfaces.

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7

Shimada, Ichiro, and De-Qi Zhang. "Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces." Nagoya Mathematical Journal 161 (March 2001): 23–54. http://dx.doi.org/10.1017/s002776300002211x.

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We present a complete list of extremal elliptic K3 surfaces (Theorem 1.1). As an application, we give a sufficient condition for the topological fundamental group of complement to an ADE-configuration of smooth rational curves on a K3 surface to be trivial (Proposition 4.1 and Theorem 4.3).

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8

Shimada, Ichiro. "On normal K3 surfaces." Michigan Mathematical Journal 55, no. 2 (August 2007): 395–416. http://dx.doi.org/10.1307/mmj/1187647000.

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9

Nishiguchi, Kenji. "Degeneration of K3 surfaces." Journal of Mathematics of Kyoto University 28, no. 2 (1988): 267–300. http://dx.doi.org/10.1215/kjm/1250520482.

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10

PARK, B. DOUG. "DOUBLING HOMOTOPY K3 SURFACES." Journal of Knot Theory and Its Ramifications 12, no. 03 (May 2003): 347–54. http://dx.doi.org/10.1142/s0218216503002469.

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We perform certain doubling operation on the homotopy K3 surfaces of R. Fintushel and R. J. Stern to obtain a new family of smooth closed simply-connected irreducible spin 4-manifolds indexed by knots in S3.

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11

Reinecke, Emanuel. "Autoequivalences of twisted K3 surfaces." Compositio Mathematica 155, no. 5 (April 30, 2019): 912–37. http://dx.doi.org/10.1112/s0010437x19007176.

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Derived equivalences of twisted K3 surfaces induce twisted Hodge isometries between them; that is, isomorphisms of their cohomologies which respect certain natural lattice structures and Hodge structures. We prove a criterion for when a given Hodge isometry arises in this way. In particular, we describe the image of the representation which associates to any autoequivalence of a twisted K3 surface its realization in cohomology: this image is a subgroup of index $1$or $2$in the group of all Hodge isometries of the twisted K3 surface. We show that both indices can occur.

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12

Nikulin, Viacheslav V. "Elliptic Fibrations on K3 Surfaces." Proceedings of the Edinburgh Mathematical Society 57, no. 1 (December 19, 2013): 253–67. http://dx.doi.org/10.1017/s0013091513000953.

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AbstractThis paper consists mainly of a review and applications of our old results relating to the title. We discuss how many elliptic fibrations and elliptic fibrations with infinite automorphism groups (or Mordell–Weil groups) an algebraic K3 surface over an algebraically closed field can have. As examples of applications of the same ideas, we also consider K3 surfaces with exotic structures: with a finite number of non-singular rational curves, with a finite number of Enriques involutions, and with naturally arithmetic automorphism groups.

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13

Taelman, Lenny. "Ordinary K3 surfaces over a finite field." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 761 (April 1, 2020): 141–61. http://dx.doi.org/10.1515/crelle-2018-0023.

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AbstractWe give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over {{\mathbf{Z}}}. This gives an analogue for K3 surfaces of Deligne’s description of the category of ordinary abelian varieties over a finite field, and refines earlier work by N.O. Nygaard and J.-D. Yu. Our main result is conditional on a conjecture on potential semi-stable reduction of K3 surfaces over p-adic fields. We give unconditional versions for K3 surfaces of large Picard rank and for K3 surfaces of small degree.

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14

Ito, Kazuhiro. "On the Supersingular Reduction of K3 Surfaces with Complex Multiplication." International Mathematics Research Notices 2020, no. 20 (September 4, 2018): 7306–46. http://dx.doi.org/10.1093/imrn/rny210.

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Abstract We study the good reduction modulo $p$ of $K3$ surfaces with complex multiplication. If a $K3$ surface with complex multiplication has good reduction, we calculate the Picard number and the height of the formal Brauer group of the reduction. Moreover, if the reduction is supersingular, we calculate its Artin invariant under some assumptions. Our results generalize some results of Shimada for $K3$ surfaces with Picard number $20$. Our methods rely on the main theorem of complex multiplication for $K3$ surfaces by Rizov, an explicit description of the Breuil–Kisin modules associated with Lubin–Tate characters due to Andreatta, Goren, Howard, and Madapusi Pera, and the integral comparison theorem recently established by Bhatt, Morrow, and Scholze.

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15

Ma, Shouhei. "On $K3$ surfaces which dominate Kummer surfaces." Proceedings of the American Mathematical Society 141, no. 1 (May 15, 2012): 131–37. http://dx.doi.org/10.1090/s0002-9939-2012-11302-4.

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16

Hulek, Klaus, and Matthias Schütt. "Enriques surfaces and Jacobian elliptic K3 surfaces." Mathematische Zeitschrift 268, no. 3-4 (April 17, 2010): 1025–56. http://dx.doi.org/10.1007/s00209-010-0708-3.

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17

TAKI, SHINGO. "SINGULARITIES OF QUOTIENT SURFACES OF K3 SURFACES." Mathematical Reports 25(75), no. 3 (2023): 413–23. http://dx.doi.org/10.59277/mrar.2023.25.75.3.413.

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18

Camere, Chiara, Grzegorz Kapustka, Michał Kapustka, and Giovanni Mongardi. "Verra Four-Folds, Twisted Sheaves, and the Last Involution." International Mathematics Research Notices 2019, no. 21 (February 1, 2018): 6661–710. http://dx.doi.org/10.1093/imrn/rnx327.

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Abstract We study the geometry of some moduli spaces of twisted sheaves on K3 surfaces. In particular we introduce induced automorphisms from a K3 surface on moduli spaces of twisted sheaves on this K3 surface. As an application we prove the unirationality of moduli spaces of irreducible holomorphic symplectic manifolds of K3[2]-type admitting non-symplectic involutions with invariant lattices U(2) ⊕ D4(−1) or U(2) ⊕ E8(−2). This complements the results obtained in [43], [13], and the results from [29] about the geometry of irreducible holomorphic symplectic (IHS) four-folds constructed using the Hilbert scheme of (1, 1) conics on Verra four-folds. As a byproduct we find that IHS four-folds of K3[2]-type with Picard lattice U(2) ⊕ E8(−2) naturally contain non-nodal Enriques surfaces.

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19

Sertöz, Alı Sınan. "Which singular K3 surfaces cover an Enriques surface." Proceedings of the American Mathematical Society 133, no. 1 (August 20, 2004): 43–50. http://dx.doi.org/10.1090/s0002-9939-04-07666-x.

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20

KNUTSEN, ANDREAS LEOPOLD. "ON TWO CONJECTURES FOR CURVES ON K3 SURFACES." International Journal of Mathematics 20, no. 12 (December 2009): 1547–60. http://dx.doi.org/10.1142/s0129167x09005881.

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We prove that the gonality among the smooth curves in a complete linear system on a K3 surface is constant except for the Donagi–Morrison example. This was proved by Ciliberto and Pareschi under the additional condition that the linear system is ample. The constancy was originally conjectured by Harris and Mumford. As a consequence we prove that exceptional curves on K3 surfaces satisfy the Eisenbud–Lange–Martens–Schreyer conjecture and explicitly describe such curves. They turn out to be natural extensions of the Eisenbud–Lange–Martens–Schreyer examples of exceptional curves on K3 surfaces.

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21

Huybrechts, Daniel, Emanuele Macrì, and Paolo Stellari. "Stability conditions for generic K3 categories." Compositio Mathematica 144, no. 1 (January 2008): 134–62. http://dx.doi.org/10.1112/s0010437x07003065.

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AbstractA K3 category is by definition a Calabi–Yau category of dimension two. Geometrically K3 categories occur as bounded derived categories of (twisted) coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there are no spherical objects (or just one up to shift). We study stability conditions on K3 categories as introduced by Bridgeland and prove his conjecture about the topology of the stability manifold and the autoequivalences group for generic twisted projective K3, abelian surfaces, and K3 surfaces with trivial Picard group.

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22

Schütt, Matthias. "Dynamics on supersingular K3 surfaces." Commentarii Mathematici Helvetici 91, no. 4 (2016): 705–19. http://dx.doi.org/10.4171/cmh/400.

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23

Huybrechts, Daniel. "Motives of isogenous K3 surfaces." Commentarii Mathematici Helvetici 94, no. 3 (September 25, 2019): 445–58. http://dx.doi.org/10.4171/cmh/465.

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24

Faenzi, Daniele. "Ulrich bundles on K3 surfaces." Algebra & Number Theory 13, no. 6 (August 18, 2019): 1443–54. http://dx.doi.org/10.2140/ant.2019.13.1443.

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25

SHIODA, Tetsuji. "K3 surfaces and sphere packings." Journal of the Mathematical Society of Japan 60, no. 4 (October 2008): 1083–105. http://dx.doi.org/10.2969/jmsj/06041083.

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26

Itenberg, Ilia, and Grigory Mikhalkin. "Area in real K3-surfaces." EMS Surveys in Mathematical Sciences 8, no. 1 (August 31, 2021): 217–35. http://dx.doi.org/10.4171/emss/48.

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27

Aspinwall, Paul S. "K3 surfaces and string duality." Surveys in Differential Geometry 5, no. 1 (1999): 1–95. http://dx.doi.org/10.4310/sdg.1999.v5.n1.a1.

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28

Sosna, Pawel. "Derived equivalent conjugate K3 surfaces." Bulletin of the London Mathematical Society 42, no. 6 (September 3, 2010): 1065–72. http://dx.doi.org/10.1112/blms/bdq065.

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29

Beauville, A., and J. Y. M�rindol. "Sections hyperplanes des surfaces $K3$." Duke Mathematical Journal 55, no. 4 (December 1987): 873–78. http://dx.doi.org/10.1215/s0012-7094-87-05541-4.

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30

Liedtke, Christian, and Yuya Matsumoto. "Good reduction of K3 surfaces." Compositio Mathematica 154, no. 1 (September 18, 2017): 1–35. http://dx.doi.org/10.1112/s0010437x17007400.

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Let $K$ be the field of fractions of a local Henselian discrete valuation ring ${\mathcal{O}}_{K}$ of characteristic zero with perfect residue field $k$. Assuming potential semi-stable reduction, we show that an unramified Galois action on the second $\ell$-adic cohomology group of a K3 surface over $K$ implies that the surface has good reduction after a finite and unramified extension. We give examples where this unramified extension is really needed. Moreover, we give applications to good reduction after tame extensions and Kuga–Satake Abelian varieties. On our way, we settle existence and termination of certain flops in mixed characteristic, and study group actions and their quotients on models of varieties.

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31

Budur, Nero, and Ziyu Zhang. "Formality conjecture for K3 surfaces." Compositio Mathematica 155, no. 5 (April 23, 2019): 902–11. http://dx.doi.org/10.1112/s0010437x19007206.

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We give a proof of the formality conjecture of Kaledin and Lehn: on a complex projective K3 surface, the differential graded (DG) algebra$\operatorname{RHom}^{\bullet }(F,F)$is formal for any sheaf$F$polystable with respect to an ample line bundle. Our main tool is the uniqueness of the DG enhancement of the bounded derived category of coherent sheaves. We also extend the formality result to derived objects that are polystable with respect to a generic Bridgeland stability condition.

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32

VAN GEEMEN, BERT, and JAAP TOP. "AN ISOGENY OF K3 SURFACES." Bulletin of the London Mathematical Society 38, no. 02 (March 16, 2006): 209–23. http://dx.doi.org/10.1112/s0024609306018170.

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33

Nikulin, V. V. "ON CORRESPONDENCES BETWEEN K3 SURFACES." Mathematics of the USSR-Izvestiya 30, no. 2 (April 30, 1988): 375–83. http://dx.doi.org/10.1070/im1988v030n02abeh001018.

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34

Kuleshov, S. A. "STABLE BUNDLES ON K3 SURFACES." Mathematics of the USSR-Izvestiya 36, no. 1 (February 28, 1991): 223–30. http://dx.doi.org/10.1070/im1991v036n01abeh001967.

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35

McMullen, Curtis T. "K3 surfaces, entropy and glue." Journal für die reine und angewandte Mathematik (Crelles Journal) 2011, no. 658 (January 2011): 1–25. http://dx.doi.org/10.1515/crelle.2011.048.

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36

Li, Jun, and Christian Liedtke. "Rational curves on K3 surfaces." Inventiones mathematicae 188, no. 3 (October 7, 2011): 713–27. http://dx.doi.org/10.1007/s00222-011-0359-y.

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37

Liedtke, Christian. "Supersingular K3 surfaces are unirational." Inventiones mathematicae 200, no. 3 (September 18, 2014): 979–1014. http://dx.doi.org/10.1007/s00222-014-0547-7.

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38

Elkies, Noam D., and Matthias Schütt. "Modular forms and K3 surfaces." Advances in Mathematics 240 (June 2013): 106–31. http://dx.doi.org/10.1016/j.aim.2013.03.008.

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39

Cheng, Miranda C. N., and Sarah Harrison. "Umbral Moonshine and K3 Surfaces." Communications in Mathematical Physics 339, no. 1 (June 25, 2015): 221–61. http://dx.doi.org/10.1007/s00220-015-2398-5.

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40

Xiao, Gang. "Galois covers between $K3$ surfaces." Annales de l’institut Fourier 46, no. 1 (1996): 73–88. http://dx.doi.org/10.5802/aif.1507.

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41

O'Grady, Kieran G. "Donaldson's polynomials for $K3$ surfaces." Journal of Differential Geometry 35, no. 2 (1992): 415–27. http://dx.doi.org/10.4310/jdg/1214448082.

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42

Oguiso, Keiji. "K3 surfaces via almost-primes." Mathematical Research Letters 9, no. 1 (2002): 47–63. http://dx.doi.org/10.4310/mrl.2002.v9.n1.a4.

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43

Bridgeland, Tom. "Stability conditions on $K3$ surfaces." Duke Mathematical Journal 141, no. 2 (February 2008): 241–91. http://dx.doi.org/10.1215/s0012-7094-08-14122-5.

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44

Bogomolov, Fedor, and Peter J. Braam. "Instantons and mirror K3 surfaces." Communications in Mathematical Physics 143, no. 3 (January 1992): 641–46. http://dx.doi.org/10.1007/bf02099270.

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45

Huybrechts, Daniel, and Paolo Stellari. "Equivalences of twisted K3 surfaces." Mathematische Annalen 332, no. 4 (June 14, 2005): 901–36. http://dx.doi.org/10.1007/s00208-005-0662-2.

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46

van Geemen, Bert, and Alessandra Sarti. "Nikulin involutions on K3 surfaces." Mathematische Zeitschrift 255, no. 4 (November 4, 2006): 731–53. http://dx.doi.org/10.1007/s00209-006-0047-6.

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47

Ballico, E., C. Fontanari, and L. Tasin. "Singular Curves on K3 Surfaces." Sarajevo Journal of Mathematics 6, no. 2 (June 11, 2024): 165–68. http://dx.doi.org/10.5644/sjm.06.2.02.

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We investigate the Clifford index of singular curves on K3 surfaces by following the lines of [10]. As a consequence, we are able to deduce from [3] that Green's conjecture holds for all integral curves on K3 surfaces. 2000 Mathematics Subject Classification. 14H51

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48

Garbagnati, Alice, and Yulieth Prieto-Montañez. "Generalized Shioda–Inose structures of order 3." Advances in Geometry 24, no. 2 (April 1, 2024): 183–207. http://dx.doi.org/10.1515/advgeom-2024-0005.

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Abstract A Shioda–Inose structure is a geometric construction which associates to an Abelian surface a projective K3 surface in such a way that their transcendental lattices are isometric. This geometric construction was described by Morrison by considering special symplectic involutions on the K3 surfaces. After Morrison several authors provided explicit examples. The aim of this paper is to generalize Morrison’s results and some of the known examples to an analogous geometric construction involving not involutions, but order 3 automorphisms. Therefore, we define generalized Shioda–Inose structures of order 3, we identify the K3 surfaces and the Abelian surfaces which appear in these structures and we provide explicit examples.

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49

Kimura, Yusuke. "F-theory models with 3 to 8 U(1) factors on K3 surfaces." International Journal of Modern Physics A 36, no. 17 (June 2, 2021): 2150125. http://dx.doi.org/10.1142/s0217751x21501256.

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In this study, we construct four-dimensional F-theory models with 3 to 8 U(1) factors on products of K3 surfaces. We provide explicit Weierstrass equations of elliptic K3 surfaces with Mordell–Weil ranks of 3 to 8. We utilize the method of quadratic base change to glue pairs of rational elliptic surfaces together to yield the aforementioned types of K3 surfaces. The moduli of elliptic K3 surfaces constructed in the study include Kummer surfaces of specific complex structures. We show that the tadpole cancels in F-theory compactifications with flux when these Kummer surfaces are paired with appropriately selected attractive K3 surfaces. We determine the matter spectra on F-theory on the pairs.

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50

Balletti, Gabriele, Marta Panizzut, and Bernd Sturmfels. "K3 polytopes and their quartic surfaces." Advances in Geometry 21, no. 1 (January 1, 2021): 85–98. http://dx.doi.org/10.1515/advgeom-2020-0016.

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Abstract K3 polytopes appear in complements of tropical quartic surfaces. They are dual to regular unimodular central triangulations of reflexive polytopes in the fourth dilation of the standard tetrahedron. Exploring these combinatorial objects, we classify K3 polytopes with up to 30 vertices. Their number is 36 297 333. We study the singular loci of quartic surfaces that tropicalize to K3 polytopes. These surfaces are stable in the sense of Geometric Invariant Theory.

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