Invariance of quantum rings under ordinary flops I: Quantum corrections and reduction to local models
Journal
Algebraic Geometry
Journal Volume
3
Journal Issue
5
Pages
578-614
Date Issued
2016
Author(s)
Abstract
This is the first of a sequence of papers proving the quantum invariance under ordinary flops over an arbitrary smooth base. In this first part, we determine the defect of the cup product under the canonical correspondence and show that it is corrected by the small quantum product attached to the extremal ray. We then perform various reductions to reduce the problem to local models. In part II ("Invariance of quantum rings under ordinary flops II", Algebraic Geometry, 2016), we develop a quantum Leray-Hirsch theorem and use it to show that the big quantum cohomology ring is invariant under analytic continuation in the Khler moduli space for ordinary flops of split type. In part III (Lee, Lin, Qu and Wang, "Invariance of quantum rings under ordinary flops III", Cambridge Journal of Mathematics, 2016), we remove the splitting condition by developing a quantum splitting principle, and hence solve the problem completely.
Type
journal article