Enumerative geometry of Calabi-Yau 4-folds
Algebraic Geometry
2008-11-26 v1 High Energy Physics - Theory
Abstract
Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation. Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including the sextic Calabi-Yau in CP5, are also studied. A complete solution of the Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic anomaly equation.
Keywords
Cite
@article{arxiv.math/0702189,
title = {Enumerative geometry of Calabi-Yau 4-folds},
author = {A. Klemm and R. Pandharipande},
journal= {arXiv preprint arXiv:math/0702189},
year = {2008}
}
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44 pages