Invariance of quantum rings under ordinary flops: III

Abstract

The paper is Part III of our ongoing project to study a case of Crepant Transformation Conjecture: K-equivalence Conjecture for ordinary flops. In this paper we prove the invariance of quantum rings for general ordinary flops, whose local models are certain non-split toric bundles over arbitrary smooth base. An essential ingredient in the proof is a quantum splitting principle, which reduces a statement in Gromov--Witten theory on non-split bundles to the case of split bundles.

References in corpus (4)

• Birational cobordism invariance of uniruled symplectic manifolds
• Stable logarithmic maps to Deligne--Faltings pairs II
• The Evaluation Space of Logarithmic Stable Maps
• Invariance of Quantum Rings under Ordinary Flops II: A quantum Leray--Hirsch theorem

Cited by in corpus (5)

• The Crepant Transformation Conjecture for Toric Complete Intersections
• On Gromov-Witten theory of projective bundles
• Invariance of Quantum Rings under Ordinary Flops II: A quantum Leray--Hirsch theorem
• A remark on virtual pushforward properties in Gromov-Witten theory
• A quantum splitting principle and an application