Results 1 to 10 of about 219 (145)
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
doaj +6 more sources
On Deformations of Toric Fano Varieties
Springer Proceedings in Mathematics and Statistics, 2022 In this note we collect some results on the deformation theory of toric Fano varieties.
Andrea Petracci, Petracci Andrea
exaly +3 more sources
Journal of Mathematical Sciences, 1999 AMSTeX, 13 pages; revised: minor typos ...
exaly +4 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
openaire +4 more sources