Results 1 to 10 of about 2,805,734 (255)
Machine learning line bundle cohomologies of hypersurfaces in toric varieties [PDF]
Physics Letters B, 2019 Different techniques from machine learning are applied to the problem of computing line bundle cohomologies of (hypersurfaces in) toric varieties. While a naive approach of training a neural network to reproduce the cohomologies fails in the general case,
Daniel Klaewer, Lorenz Schlechter
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Vanishing theorems on toric varieties [PDF]
Tohoku Mathematical Journal, 2002 We use Cox's description for sheaves on toric varieties and results about the local cohomology with respect to monomial ideals to give a characteristic free approach to vanishing results on arbitrary toric varieties. As an application, we give a proof of a strong form of Fujita's conjecture in the case of toric varieties. We also prove that every sheaf
Mircea Mustata
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Degenerations of toric ideals and toric varieties
Journal of Mathematical Analysis and Applications, 2012 Motivated by both theoretical and applied importance, the paper establishes the correspondence between the degenerations of toric ideals and the degenerations of their toric varieties when the weight admits a regular subdivision. The main result generalizes to the complex case the author's previous result jointly obtained with L.
Chun-Gang Zhu
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Communications in AlgebraIn this article, we provide characterizations of toric Richardson varieties across all types through three distinct approaches: 1) poset theory, 2) root theory, and 3) geometry.
Mahir Bilen Can, Pinakinath Saha
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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
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Discriminants of toric varieties [PDF]
Communications in Algebra, 2021 We study the subvariety of singular sections, the discriminant, of a base point free linear system $|L|$ on a smooth toric variety $X$. On one hand we describe pairs $(X,L)$ for which the discriminant is of low dimension. Precisely, we collect some bounds on this dimension and classify those pairs whose dimension differs the bound less than or equal to
Muñoz, Roberto, Nolla, Álvaro
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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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Uniform K-stability of polarized spherical varieties [PDF]
Épijournal de Géométrie Algébrique, 2023 We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties.
Thibaut Delcroix
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Toric difference variety [PDF]
Journal of Systems Science and Complexity, 2017 In this paper, the concept of toric difference varieties is defined and four equivalent descriptions for toric difference varieties are presented in terms of difference rational parametrization, difference coordinate rings, toric difference ideals, and group actions by difference tori.
Xiao-Shan Gao +3 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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