Balloon Animal Maps with Applications to the Cohomology of Hypertoric Hitchin Systems

2025/09/15 by Sundbo, Evan
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.12368

Abstract

In this article we introduce the notion of a balloon animal map between broken toric varieties and construct several long exact sequences in cohomology related to them. We give a new proof of the deletion-contraction relation on hypertoric Hitchin systems of Dansco-Mcbreen-Shende and present some refinements of it. The end result is a formula for the Poincaré polynomial of any hypertoric Hitchin system associated to a graph with first Betti number 2 along with a recipe to calculate the Poincaré polynomial of any hypertoric Hitchin system, given knowledge of a finite number of base cases.

Citations

• Equivariant K-theory, affine Grassmannian and perfection
• Broken Toric Varieties and Cell-Compatible Sheaves
• Persistent sheaf cohomology
• Deletion-contraction triangles for Hausel-Proudfoot varieties
• Sheaves, Cosheaves and Applications
• Multiplicative preprojective algebras, middle convolution and the Deligne-Simpson problem
• Lie Group Valued Moment Maps

Related

• Hypertoric Hitchin systems and Kirchhoff polynomials
• Algebraic cycles and Hitchin systems
• Bigraded Polynomials for the Cohomology of Wild Hitchin Systems
• The Topology and Geometry of Hyperkähler Quotients
• Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams