Toric reduction and a conjecture of Batyrev and Materov

By András Szenes, Michèle Vergne. 2003

107 citations recorded by the source corpus.

We present a new integration formula for intersection numbers on toric quotients, extending the results of Witten, Jeffrey and Kirwan on localization. Our work was motivated by the Toric Residue Mirror Conjecture of Batyrev and Materov; as an application of our integration formula, we obtain a proof of this conjecture in a generalized setting.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4fd2bf62bdea87b7b6808a99384d2ba9e89d168c

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In Algebra and Number Theory

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Citations in the corpus

Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$N=2 Gauge Theories with Rank-One Gauge Groups (2013, methodology): “s vlie on a half-space and the ambient space V//Gis compact, this cycle is given as a sum of Tr’s around all unordered choices of rhyperplanes vi1(z) = 0, vi2(z) = 0, ..., vir(z) = 0, as explained in [33]. In the following, we treat a representation Ras a vector bundle whose Chern roots are w(z). Th”
Witten index and wall crossing (2014, methodology): “Qil is the defining property of the JK residue [45] (See [40] for a review).”
A topologically twisted index for three-dimensional supersymmetric theories (2015, methodology): “In many cases, we can formulate the result of integration in terms of a geometrical operation called the Jeffrey-Kirwan residue [9] (see also [10, 11]).”
QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, background): “Integrals over toric varieties may be computed via residues, as in for example Szenes-Vergne [25].”
Applications of Equivariant Cohomology (2006, unknown): “We gave in [45] a representative for the r-dimensional cycle Z(c) in C as the set of solutions of r real analytic equations related to quantum cohomology.”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “For degenerate singularities where more than rk(G) hyperplane meets, we refer to the prescription in [6, 68, 69] for an algorithmic determination of the JK contour.”