Virtual class of zero loci and mirror theorems

DOI10.4310/ATMP.2003.V7.N6.A5zbMATH Open1078.14080arXivmath/0307386MaRDI QIDQ701900

Artur Elezi

Publication date: 14 January 2005

Published in: Advances in Theoretical and Mathematical Physics (Search for Journal in Brave)

Abstract: Let $Y$ be the zero loci of a regular section of a convex vector bundle $E$ over $X$. We provide a new proof of a conjecture of Cox, Katz and Lee for the virtual class of the genus zero moduli of stable maps to $Y$. This in turn yields the expected relationship between Gromov-Witten theories of $Y$ and $X$ which together with Mirror Theorems allows for the calculation of enumerative invariants of $Y$ inside of $X$.

Full work available at URL: https://arxiv.org/abs/math/0307386

Mathematics Subject Classification ID

Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35)

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