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Quantum flips I: local model
- Source :
- Integrability, Quantization, and Geometry, dedicated to Boris Dubrovin, Vol. II, pp. 303-352, Proc. Symp. Pure Math. 103.2, AMS, 2021
- Publication Year :
- 2019
-
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 Poincar\'e 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.<br />Comment: 50 pages; v2: typos fixed
- Subjects :
- Mathematics - Algebraic Geometry
14N35, 14E30
Subjects
Details
- Database :
- arXiv
- Journal :
- Integrability, Quantization, and Geometry, dedicated to Boris Dubrovin, Vol. II, pp. 303-352, Proc. Symp. Pure Math. 103.2, AMS, 2021
- Publication Type :
- Report
- Accession number :
- edsarx.1912.03012
- Document Type :
- Working Paper