Results 1 to 10 of about 10,755 (178)
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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Gorenstein spherical Fano varieties [PDF]
Geometriae Dedicata, 2015 We obtain a combinatorial description of Gorenstein spherical Fano varieties in terms of certain polytopes, generalizing the combinatorial description of Gorenstein toric Fano varieties by reflexive polytopes and its extension to Gorenstein horospherical
Gagliardi, Giuliano +1 more
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Gorenstein toric Fano varieties [PDF]
manuscripta mathematica, 2004 We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry.
Avram +20 more
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Fano symmetric varieties with low rank
Publications of the Research Institute for Mathematical Sciences, 2010 The symmetric projective varieties of rank one are all smooth and Fano by a classic result of Akhiezer. We classify the locally factorial (respectively smooth) projective symmetric $G$-varieties of rank 2 which are Fano.
Ruzzi, Alessandro
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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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Fano and Weak Fano Hessenberg Varieties
Michigan Mathematical Journal, 2023 Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain the flag variety itself and the permutohedral variety which is a toric variety. We give a complete classification of Fano and weak Fano regular semisimple Hessenberg varieties in type A in terms of combinatorics of Hessenberg functions.
Abe, Hiraku, Fujita, Naoki, Zeng, Haozhi
openaire +3 more sources
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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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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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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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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