2020/06/17 by Rongxiao Mi, Mark Shoemaker, Mi, Rongxiao +1
Mathematics · #14E16 #14N35 #53D45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2006.09907
openalex publication_date 2020/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two varieties Z and \widetilde Z are said to be related by extremal transition if there exists a degeneration from Z to a singular variety Z and a crepant resolution \widetilde Z → Z. In this paper we compare the genus-zero Gromov--Witten theory of toric hypersurfaces related by extremal transitions arising from toric blow-up. We show that the quantum D-module of \widetilde Z, after analytic continuation and restriction of a parameter, recovers the quantum D-module of Z. The proof provides a geometric explanation for both the analytic continuation and restriction parameter appearing in the theorem.