Stringy Chern classes of singular toric varieties and their applications

Batyrev, Victor V.; Schaller, Karin

doi:10.48550/arxiv.1607.04135

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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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Section: Introductionmentioning

confidence: 86%

Global spectra, polytopes and stacky invariants

Douai

2017

Math. Z.

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Stringy Chern classes of singular toric varieties and their applications

Cited by 1 publication

References 0 publications

Global spectra, polytopes and stacky invariants

Global spectra, polytopes and stacky invariants

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