Cylinders in Fano varieties [PDF]
EMS Surveys in Mathematical Sciences, 2021 This paper is a survey about cylinders in Fano varieties and related problems.
Ivan Cheltsov +3 more
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Asymptotic Chow Semistability Implies Ding Polystability for Gorenstein Toric Fano Varieties
Mathematics, 2023 In this paper, we prove that if a Gorenstein toric Fano variety (X,−KX) is asymptotically Chow semistable, then it is Ding polystable with respect to toric test configurations (Theorem 3).
Naoto Yotsutani
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Finite $F$-representation type for homogeneous coordinate rings of non-Fano varieties [PDF]
Épijournal de Géométrie Algébrique, 2023 Finite $F$-representation type is an important notion in characteristic-$p$ commutative algebra, but explicit examples of varieties with or without this property are few.
Devlin Mallory
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Simplicity of tangent bundles of smooth horospherical varieties of Picard number one
Comptes Rendus. Mathématique, 2022 Recently, Kanemitsu has discovered a counterexample to the long-standing conjecture that the tangent bundle of a Fano manifold of Picard number one is (semi)stable. His counterexample is a smooth horospherical variety.
Hong, Jaehyun
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FANO HYPERSURFACES WITH ARBITRARILY LARGE DEGREES OF IRRATIONALITY
Forum of Mathematics, Sigma, 2020 We show that complex Fano hypersurfaces can have arbitrarily large degrees of irrationality. More precisely, if we fix a Fano index $e$, then the degree of irrationality of a very general complex Fano hypersurface of index $e$ and dimension n is bounded ...
NATHAN CHEN, DAVID STAPLETON
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Super-rigid affine Fano varieties [PDF]
Compositio Mathematica, 2018 We study a wide class of affine varieties, which we call affine Fano varieties. By analogy with birationally super-rigid Fano varieties, we define super-rigidity for affine Fano varieties, and provide many examples and non-examples of super-rigid affine Fano varieties.
Cheltsov, Ivan +2 more
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X‐ray magnetic circular dichroism
Major Reference Works, Page 508-515., 2022 International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.
Each of the eight volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the ...
Gerrit van der Laan C. Chantler +2 more
wiley +1 more source
Good reduction of Fano threefolds and sextic surfaces [PDF]
, 2017 We investigate versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings, for other classes of varieties. We first obtain analogues for certain Fano threefolds. We use these results to prove the Shafarevich conjecture
Javanpeykar, Ariyan, Loughran, Daniel
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Maximal lengths of exceptional collections of line bundles [PDF]
, 2010 In this paper we construct infinitely many examples of toric Fano varieties with Picard number three, which do not admit full exceptional collections of line bundles. In particular, this disproves King's conjecture for toric Fano varieties.
Alexander I. Efimov +9 more
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Hilbert series, machine learning, and applications to physics
Physics Letters B, 2022 We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ∼1 mean absolute error, whilst classifiers predict dimension and Gorenstein ...
Jiakang Bao +5 more
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