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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Derived categories of toric Fano 3-folds via the Frobenius morphism [PDF]
Le Matematiche, 2009 In [8, Conjecture 3.6], Costa and Miró-Roig state the following conjecture:Every smooth complete toric Fano variety has a full strongly exceptional collection of line bundles. The goal of this article is to prove it for toric Fano 3-folds.
Alessandro Bernardi, Sofia Tirabassi
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Nonsolidity of uniruled varieties
Forum of Mathematics, Sigma, 2023 We give conditions for a uniruled variety of dimension at least 2 to be nonsolid. This study provides further evidence to a conjecture by Abban and Okada on the solidity of Fano 3-folds.
Livia Campo, Tiago Duarte Guerreiro
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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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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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Variation of stable birational types in positive characteristic [PDF]
Épijournal de Géométrie Algébrique, 2020 Let k be an uncountable algebraically closed field and let Y be a smooth projective k-variety which does not admit a decomposition of the diagonal. We prove that Y is not stably birational to a very general hypersurface of any given degree and dimension.
Stefan Schreieder
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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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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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Fibers over infinity of Landau-Ginzburg models [PDF]
, 2020 We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety $X$ equals the dimension of the anticanonical system of $X$.
Cheltsov, Ivan, Przyjalkowski, Victor
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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