Stringy Chern classes of singular toric varieties and their applications

Batyrev, Victor V.; Schaller, Karin

doi:10.4310/cntp.2017.v11.n1.a1

Cited by 10 publications

(8 citation statements)

References 10 publications

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“…Note that we are not studying the orbifold or stringy topological quantities associated to the singular variety as has been done in[75][76][77].…”

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confidence: 99%

Calabi–Yau Volumes and Reflexive Polytopes

He¹,

Seong²,

Yau³

2018

Commun. Math. Phys.

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We study various geometrical quantities for Calabi-Yau varieties realized as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. Focus is made on reflexive polytopes up to dimension 4 and the minimized volumes of the Sasaki-Einstein base of the corresponding Calabi-Yau cone are calculated. By doing so, we conjecture new bounds for the Sasaki-Einstein volume with respect to various topological quantities of the corresponding toric varieties. We give interpretations about these volume bounds in the context of associated field theories via the AdS/CFT correspondence.

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“…Note that we are not studying the orbifold or stringy topological quantities associated to the singular variety as has been done in[75][76][77].…”

mentioning

confidence: 99%

Calabi–Yau Volumes and Reflexive Polytopes

He¹,

Seong²,

Yau³

2018

Commun. Math. Phys.

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“…which is a generalization of formula (5): indeed, a reflexive polytope P is Fano and its geometric spectrum satisfies µ i=1 (α i − 1) 2 = 2 (after a preprint version of this paper was written [8], I have been informed that an analogous result was proposed independently by Batyrev and Schaller in [3]).…”

Section: Introductionmentioning

confidence: 86%

Global spectra, polytopes and stacky invariants

Douai

2017

Math. Z.

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Given a convex polytope, we define its geometric spectrum, a stacky version of Batyrev's stringy E-functions, and we prove a stacky version of a formula of Libgober and Wood about the E-polynomial of a smooth projective variety. As an application, we get a closed formula for the variance of the geometric spectrum and a Noether's formula for two dimensional Fano polytopes (polytopes whose vertices are primitive lattice points; a Fano polytope is not necessarily smooth). We also show that this geometric spectrum is equal to the algebraic spectrum (the spectrum at infinity of a tame Laurent polynomial whose Newton polytope is the polytope alluded to). This gives an explanation and some positive answers to Hertling's conjecture about the variance of the spectrum of tame regular functions. * Partially supported by the grant ANR-13-IS01-0001-01 of the Agence nationale de la recherche. Mathematics Subject Classification 32S40, 14J33, 34M35, 14C40. Key words and phrases: Mirror symmetry, toric varieties, polytopes, orbifold cohomology, spectrum of regular tame functions. Y , with primitive generators v 1 , · · · , v r and associated divisors D 1 , · · · , D r . Put, for a subset J ⊂ I := {1, · · · , r}, D J := ∩ j∈J D j if J = ∅ and D J := Y if J = ∅ and define E st,P (z) := J⊂I

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“…In what follows, we will focus on the so called stringy topological data as originally introduced by Batyrev in the context of reflexive polytopes, ∆, and the associated toric varieties, X ∆ [7,47,48]. 4 The main idea is that certain topological invariants, including the Hodge numbers and in particular the Euler number, are independent of the choice of the so called crepant desingularization of X ∆ [50,51].…”

Section: Analytic Formulaementioning

confidence: 99%

“…Libgober and Wood showed that there exists an identity relating c 1 (X)c n−1 (X) and the Hodge numbers, h p,q (X) for X a smooth projective variety [52]. This was generalized by Batyrev, et al to any toric variety X ∆ associated to a reflexive polytope ∆ in terms of the combinatorial data of ∆ [7,47,48],…”

Section: Analytic Formulaementioning

confidence: 99%

Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds

Berglund¹,

Campbell²,

Jejjala³

2021

Preprint

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Using a fully connected feedforward neural network we study topological invariants of a class of Calabi-Yau manifolds constructed as hypersurfaces in toric varieties associated with reflexive polytopes from the Kreuzer-Skarke database. In particular, we find the existence of a simple expression for the Euler number that can be learned in terms of limited data extracted from the polytope and its dual.

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Stringy Chern classes of singular toric varieties and their applications

Cited by 10 publications

References 10 publications

Calabi–Yau Volumes and Reflexive Polytopes

Calabi–Yau Volumes and Reflexive Polytopes

Global spectra, polytopes and stacky invariants

Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds

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