On Fano Schemes of Toric Varieties [PDF]
SIAM Journal on Applied Algebra and Geometry, 2017 Let $X_\mathcal{A}$ be the projective toric variety corresponding to a finite set of lattice points $\mathcal{A}$. We show that irreducible components of the Fano scheme $\mathbf{F}_k(X_\mathcal{A})$ parametrizing $k$-dimensional linear subspaces of $X_\mathcal{A}$ are in bijection to so-called maximal Cayley structures for $\mathcal{A}$. We explicitly
Nathan Owen Ilten, Alexandre Zotine
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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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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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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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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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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
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Invariants of Fano Varieties in Families [PDF]
Moscow Mathematical Journal, 2018 11 pages. Corrected mistake in appendix.
Gounelas, Frank, Javanpeykar, Ariyan
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On the classification of toric fano varieties [PDF]
Discrete & Computational Geometry, 1988 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Hilbert series, machine learning, and applications to physics
Physics Letters B, 2022 We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ∼1 mean absolute error, whilst classifiers predict dimension and Gorenstein ...
Jiakang Bao +5 more
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A proposal for (0,2) mirrors of toric varieties
Journal of High Energy Physics, 2017 In this paper we propose (0,2) mirrors for general Fano toric varieties with special tangent bundle deformations, corresponding to subsets of toric deformations.
Wei Gu, Eric Sharpe
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