Relevant bibliographies by topics / Fano threefold

Academic literature on the topic 'Fano threefold'

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Published: 14 March 2023

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Journal articles on the topic "Fano threefold"

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Cheltsov, Ivan, and Jihun Park. "Birationally rigid Fano threefold hypersurfaces." Memoirs of the American Mathematical Society 246, no. 1167 (March 2017): 0. http://dx.doi.org/10.1090/memo/1167.

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Polishchuk, A. "Simple Helices on Fano Threefolds." Canadian Mathematical Bulletin 54, no. 3 (September 1, 2011): 520–26. http://dx.doi.org/10.4153/cmb-2010-106-x.

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AbstractBuilding on the work of Nogin, we prove that the braid groupB4acts transitively on full exceptional collections of vector bundles on Fano threefolds withb2= 1 andb3= 0. Equivalently, this group acts transitively on the set of simple helices (considered up to a shift in the derived category) on such a Fano threefold. We also prove that on threefolds withb2= 1 and very ample anticanonical class, every exceptional coherent sheaf is locally free.
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Zhang, De-Qi. "Polarized endomorphisms of uniruled varieties. With an appendix by Y. Fujimoto and N. Nakayama." Compositio Mathematica 146, no. 1 (December 21, 2009): 145–68. http://dx.doi.org/10.1112/s0010437x09004278.

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AbstractWe show that polarized endomorphisms of rationally connected threefolds with at worst terminal singularities are equivariantly built up from those on ℚ-Fano threefolds, Gorenstein log del Pezzo surfaces and ℙ1. Similar results are obtained for polarized endomorphisms of uniruled threefolds and fourfolds. As a consequence, we show that every smooth Fano threefold with a polarized endomorphism of degree greater than one is rational.
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Furushima, Mikio, and Noboru Nakayama. "The family of lines on the Fano threefold V5." Nagoya Mathematical Journal 116 (December 1989): 111–22. http://dx.doi.org/10.1017/s0027763000001719.

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A smooth projective algebraic 3-fold V over the field C is called a Fano 3-fold if the anticanonical divisor — Kv is ample. The integer g = g(V) = ½(- Kv)3 is called the genus of the Fano 3-fold V. The maximal integer r ≧ 1 such that ϑ(— Kv)≃ ℋ r for some (ample) invertible sheaf ℋ ε Pic V is called the index of the Fano 3-fold V. Let V be a Fano 3-fold of the index r = 2 and the genus g = 21 which has the second Betti number b2(V) = 1. Then V can be embedded in P6 with degree 5, by the linear system |ℋ|, where ϑ(— Kv)≃ ℋ2 (see Iskovskih [5]). We denote this Fano 3-fold V by V5.
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Segal, Ed, and Richard Thomas. "Quintic threefolds and Fano elevenfolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 743 (October 1, 2018): 245–59. http://dx.doi.org/10.1515/crelle-2015-0108.

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Abstract The derived category of coherent sheaves on a general quintic threefold is a central object in mirror symmetry. We show that it can be embedded into the derived category of a certain Fano elevenfold. Our proof also generates related examples in different dimensions.
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Cheltsov, Ivan, and Jihun Park. "Halphen pencils on weighted Fano threefold hypersurfaces." Open Mathematics 7, no. 1 (January 1, 2009): 1–45. http://dx.doi.org/10.2478/s11533-008-0056-2.

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AbstractOn a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.
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Faenzi, Daniele. "Bundles over the Fano Threefold V 5." Communications in Algebra 33, no. 9 (August 2005): 3061–80. http://dx.doi.org/10.1081/agb-200066116.

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Ishikawa, Daizo. "Weak Fano bundles on the cubic threefold." Manuscripta Mathematica 149, no. 1-2 (June 9, 2015): 171–77. http://dx.doi.org/10.1007/s00229-015-0763-5.

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CIOLLI, GIANNI. "ON THE QUANTUM COHOMOLOGY OF SOME FANO THREEFOLDS AND A CONJECTURE OF DUBROVIN." International Journal of Mathematics 16, no. 08 (September 2005): 823–39. http://dx.doi.org/10.1142/s0129167x05003144.

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In the present paper the small quantum cohomology ring of some Fano threefolds which are obtained as one- or two-curve blow-ups from ℙ3or the quadric Q3is explicitely computed. Because of systematic usage of the associativity property of quantum product only a very small and enumerative subset of Gromov–Witten invariants is needed. Then, for these threefolds the Dubrovin conjecture on the semisimplicity of quantum cohomology is proven by checking the computed quantum cohomology rings and by showing that a smooth Fano threefold X with b3(X) = 0 admits a complete exceptional set of the appropriate length.
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HÖRING, ANDREAS. "MINIMAL CLASSES ON THE INTERMEDIATE JACOBIAN OF A GENERIC CUBIC THREEFOLD." Communications in Contemporary Mathematics 12, no. 01 (February 2010): 55–70. http://dx.doi.org/10.1142/s0219199710003737.

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Let X be a smooth cubic threefold. We can associate two objects to X: the intermediate Jacobian J and the Fano surface F parametrizing lines on X. By a theorem of Clemens and Griffiths, the Fano surface can be embedded in the intermediate Jacobian and the cohomology class of its image is minimal. In this paper, we show that if X is generic, the Fano surface is the only surface of minimal class in J.
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Dissertations / Theses on the topic "Fano threefold"

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Karzhemanov, Ilya. "Fano threefolds and algebraic families of surfaces of Kodaira dimension zero." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/33321.

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The thesis consists of four chapters. First chapter is introductory. In Chapter 2, we recall some basic facts from the singularity theory of algebraic varieties (see Section 2.2) and the theory of minimal models (see Section 2.3), which will be used throughout the rest of the thesis. We also make some conventions on the notions and notation used in the thesis (see Section 2.1). Each Chapter 3 and 4 starts with some preliminary results (see Sections 3.1 and 4.1, respectively). Each Chapter 3 and 4 ends with some corollaries and conclusive remarks (see Sections 3.7 and 4.4, respectively). In Chapter 3, we prove Theorem 1.2.7, providing the complete description of Halphen pencils on a smooth projective quartic threefold X in P4. Let M be such a pencil. Firstly, we show that M ⊂ | − nKX | for some n ∈ N, and the pair (X,1n M) is canonical but not terminal. Further, if the set of not terminal centers CS(X, 1 ) (see Remark 2.2.8) does not contain points, we show that n = 1 (see Section 3.2). Finally, if there is a point P ∈ CS(X, n M), in Section 3.1 we show first that a general M ∈ M has multiplicity 2n at P (cf. Example 1.2.3). After that, analyzing the shape of the Hessian of the equation of X at the point P , we prove that n = 2 and M coincides with the exceptional Halphen pencil from Example 1.2.6 (see Sections 3.3-3.6). In Chapter 4, we prove Theorem 1.2.11, which shows, in particular, that a general smooth K3 surfaces of type R is an anticanonical section of the Fano threefold X with canonical Gorenstein singularities and genus 36. In Section 4.2, we prove that X is unique up to an isomorphism and has a unique singular point, providing the geometric quotient construction of the moduli space F in Section 4.3 (cf. Remark 1.2.12). Finally, in Section 4.3 we prove that the forgetful map F −→ KR is generically surjective.
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Books on the topic "Fano threefold"

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Park, Jihun, and Ivan Cheltsov. Birationally Rigid Fano Threefold Hypersurfaces. American Mathematical Society, 2017.

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Book chapters on the topic "Fano threefold"

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Abban, Hamid, Ivan Cheltsov, and Jihun Park. "On Geometry of Fano Threefold Hypersurfaces." In Rationality of Varieties, 1–14. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-75421-1_1.

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Conte, A. "Fano threefolds with singularities." In Lecture Notes in Mathematics, 71–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074996.

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Petracci, Andrea. "An Example of Mirror Symmetry for Fano Threefolds." In Birational Geometry and Moduli Spaces, 173–88. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37114-2_10.

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Hassett, Brendan, and Yuri Tschinkel. "Rationality of Fano Threefolds of Degree 18 over Non-closed Fields." In Rationality of Varieties, 237–47. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-75421-1_9.

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"Fano threefolds as hyperplane sections." In Projective Varieties with Unexpected Properties, edited by Ciro Ciliberto, Antony V. Geramita, Brian Harbourne, Rosa Maria Miró-Roig, and Kristian Ranestad. Berlin, New York: Walter de Gruyter, 2005. http://dx.doi.org/10.1515/9783110199703.19.

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Prokhorov, Yuri. "Rationality of Q-Fano Threefolds of Large Fano Index." In Recent Developments in Algebraic Geometry, 253–74. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781009180849.009.

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MANIN, YU I. "Notes on the arithmetic of Fano threefolds." In World Scientific Series in 20th Century Mathematics, 408–26. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789812830517_0020.

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Conference papers on the topic "Fano threefold"

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Richardson, D., H. M. Gibbs, and S. W. Koch. "Computer simulations of fully cascadable picosecond all-optical logic using nonlinear semiconductor étalons." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.wb4.

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Nonlinear Fabry-Perot étalons have been studied vigorously in recent years as potential all-optical decision-making elements. Fundamental physical and engineering tradeoffs have thus far prevented their use in real-world systems. Bistable devices can be cascaded at megahertz rates but require strong holding powers and fail to demonstrate useful gain for subnanosecond pulses. Two-wavelength logic-gate étalons can switch in picoseconds with picojoule energies but have thus far proved difficult to cascade. In this talk we propose a paired semiconductor étalon scheme that attempts to solve these problems, and we present the results of computer simulations of the device concept. In the envisioned architecture a two-wavelength NOR-gate étalon is operated in series with an "upconverter" étalon to allow cascadable operation on a picosecond timescale. The paired device is predicted to achieve a fan-out of at least 2 and good overall contrast, requiring about 75 pj to perform a single logic operation/upconversion. Related simulations indicate that the NOR-gate étalon itself requires a minimum of 28 pJ to achieve the same contrast and fan-out. Thus the price for cascadability is basically a threefold increase in input energy over the NOR-gate alone. The energy requirement might be reduced through the use of multiple-quantum-well materials. The computer simulations of the device behavior are based on a realistic model for the carrier-density-dependent optical nonlinearities of bulk GaAs.
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Zawislak, Maverick, and Michael Birk. "Experimental Drag and Mixing From Lobed Nozzles Under High Swirl Conditions From a Ducted Fan." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-15211.

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Abstract The availability of aerodynamic performance and vorticity production data from mixers under swirl was a challenge for future full-scale design and CFD validation. This paper presents an experimental comparison of drag and mixing performance of a circular trialing edge, lobed nozzle and scalloped nozzle under high swirl conditions as produced by a ducted fan in a subsonic wind tunnel. The design methodology is shared in detail allowing for geometry reproduction. Swirl angles produced by the fan naturally varied between 12° up to 45° according to a free-vortex profile. Performance is compared in terms of net thrust, uniformity factor and vorticity production as measured by 6-component loadcells and a seven-hole pressure probe traverse. The goal of this work was threefold: to study the axial and normal vorticity production from mixers produced by the design methodology, a preliminary investigation into lobed mixers potential in engine plume cooling and to provide a data set for RANS-CFD validation. A better understanding of lobed mixer mixing mechanisms relative to performance is offered. It is shown that the change in minimum throttle to achieve forward thrust varied between devices as did the twist load due to angular forces. A 4% reduction in required fan power to achieve forward thrust was achieved with the lobed mixer. Furthermore, maximum net thrust increased up to 20% with the mixing nozzles compared to the standard round nozzle suggesting flow straightening can lead to thrust gain in high swirling jet flows to a level that counters increases in drag. Axial and normal vorticity were clearly identified. Co-rotating vortex pairs were produced by the mixers of physical size proportional to the lobe height and wavelength. Axial vorticity levels integrated up to 110% of the round nozzle and occupied 5 times the area. Similarly, integrated normal vorticity increased up to 80% over an area 120% larger. Uniformity factor was best for the scalloped mixer due to enhanced mass flow entrainment through the notch and not the vortex production itself.
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