Year: 2019
Type: preprint
Abstract: We study analytic continuations of quantum cohomology under simple flips $f: X \dashrightarrow X'$ along the extremal ray quantum variable $q^\ell$. The inverse correspondence $Ψ= [Γ_f]^*$ by the graph closure gives an embedding of Chow motives $[\hat{X}'] \hookrightarrow [\hat{X}]$ which preserves the Poincaré pairing. We construct a deformation $\widehatΨ$ of $Ψ= [Γ_f]^*$ which induces a non-linear embedding $$QH(X') \hookrightarrow QH(X)$$ in the category of $F$-manifolds into the regular integrable loci of $QH(X)$ near $q^\ell = \infty$. This provides examples of functoriality of quantum cohomology beyond $K$-equivalent transformations. In this paper, we focus on the case when $X$ and $X'$ are (projective) local models.
Source: arXiv (Cornell University)
Authors: Lee, Yuan-Pin, Lin, Hui-Wen, Wang, Chin-Lung
Institution: National Taiwan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2993800751