Quantum flips I: local model
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 $\Psi = [\Gamma_f]^*$ by the graph closure gives an embedding of Chow motives $[\hat{X}'] \hookrightarrow [\hat{X}]$ which preserves the Poincaré pairing. We construct a deformation $\widehat{\Psi}$ of $\Psi = [\Gamma_f]^*$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2019
- DOI:
- 10.48550/arXiv.1912.03012
- arXiv:
- arXiv:1912.03012
- Bibcode:
- 2019arXiv191203012L
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14N35;
- 14E30
- E-Print:
- 50 pages