Generalized Calabi-Yau structures, K3 surfaces, and B-fields
摘要
Generalized Calabi-Yau structures, a notion recently introduced by Hitchin, are studied in the case of K3 surfaces. We show how they are related to the classical theory of K3 surfaces and to moduli spaces of certain SCFT as studied by Aspinwall and Morrison. It turns out that K3 surfaces and symplectic structures are both special cases of this general notion. The moduli space of generalized Calabi-Yau structures admits a canonical symplectic form with respect to which the moduli space of symplectic structures is Lagrangian. The standard theory of K3 surfaces implies surjectivity of the period map and a weak form of the Global Torelli theorem.
引用
@article{arxiv.math/0306162,
title = {Generalized Calabi-Yau structures, K3 surfaces, and B-fields},
author = {Daniel Huybrechts},
journal= {arXiv preprint arXiv:math/0306162},
year = {2013}
}
备注
24 pages. This final version of the paper, to appear in Int.J.Math., contains further comments on N=(2,2) susy, the definition of twisted Picard and transcendental lattice, and a review of Caldararu's conjecture on the equivalence of twisted derived categories