Toric reduction and a conjecture of Batyrev and Materov

2003/06/30 by András Szenes, Andras Szenes, Michèle Vergne +1 · 3 citations
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complete intersection #Conjecture #Differential equation #Geometry #Intersection (aeronautics) #Intersection theory #Mathematical analysis #Mathematics #Polynomial and algebraic computation #Pure mathematics #Quotient #Reduction (mathematics) #Toric variety #math.AG #math.AT

paper · pdf · doi:10.1007/s00222-004-0375-2

42 pages, latex; references added, exposition improved

arxiv created 2004/02/20 · openalex publication_date 2004/06/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Principles of Algebraic Geometry
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Differential Forms in Algebraic Topology
• Two Dimensional Gauge Theories Revisited
• Toric Hyperkahler Varieties
• Toric residues

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