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Regular version of the site

Book chapter

Degenerations, transitions and quantum cohomology

P. 1269-1273.

Given a singular variety I discuss the relations between quantum cohomology of its resolution and smoothing. In particular, I explain how toric degenerations help with computing Gromov–Witten invariants, and the role of this story in “Fanosearch” programme. The challenge is to formulate enumerative symplectic geometry of complex 3-folds in a way suitable for extracting invariants under blowups, contractions, and transitions.