Genus zero Gopakumar-Vafa invariants of the Banana manifold

2019/09/04 by Nina Morishige, Morishige, Nina
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1909.01540

Abstract

The Banana manifold X_Ban is a compact Calabi-Yau threefold constructed as the conifold resolution of the fiber product of a generic rational elliptic surface with itself, first studied by Bryan. We compute Katz's genus 0 Gopakumar-Vafa invariants of fiber curve classes on the Banana manifold X_Ban→ P¹. The weak Jacobi form of weight -2 and index 1 is the associated generating function for these genus 0 Gopakumar-Vafa invariants. The invariants are shown to be an actual count of structure sheaves of certain possibly nonreduced genus 0 curves on the universal cover of the singular fibers of X_Ban→ P¹.

Related

• Genus zero Gopakumar-Vafa invariants of Multi-Banana configurations
• An Introduction to Modern Enumerative Geometry with Applications to the Banana Manifold
• Genus zero Gopakumar-Vafa invariants of contractible curves
• The Enumerative Geometry and Arithmetic of Banana Nano-Manifolds
• The Donaldson-Thomas partition function of the banana manifold