Results 1 to 10 of about 10,805 (174)
Machine learning the dimension of a Fano variety [PDF]
Nature Communications, 2023 Fano varieties are basic building blocks in geometry – they are ‘atomic pieces’ of mathematical shapes. Recent progress in the classification of Fano varieties involves analysing an invariant called the quantum period.
Tom Coates +2 more
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On the minimal model program for projective varieties with pseudo-effective tangent sheaf [PDF]
Épijournal de Géométrie Algébrique, 2023 In this paper, we develop a theory of pseudo-effective sheaves on normal projective varieties. As an application, by running the minimal model program, we show that projective klt varieties with pseudo-effective tangent sheaf can be decomposed into Fano ...
Shin-ichi Matsumura
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Rationally connected rational double covers of primitive Fano varieties [PDF]
Épijournal de Géométrie Algébrique, 2020 We show that for a Zariski general hypersurface $V$ of degree $M+1$ in ${\mathbb P}^{M+1}$ for $M\geqslant 5$ there are no Galois rational covers $X\dashrightarrow V$ of degree $d\geqslant 2$ with an abelian Galois group, where $X$ is a rationally ...
Aleksandr V. Pukhlikov
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Kähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One
Mathematics, 2021 Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler–Einstein metrics ...
Jae-Hyouk Lee +2 more
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Affine Subspace Concentration Conditions [PDF]
Épijournal de Géométrie Algébrique, 2023 We define a new notion of affine subspace concentration conditions for lattice polytopes, and prove that they hold for smooth and reflexive polytopes with barycenter at the origin.
Kuang-Yu Wu
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K-stability of Fano varieties via admissible flags
Forum of Mathematics, Pi, 2022 We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces ...
Hamid Abban, Ziquan Zhuang
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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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