Generalized Calabi-Yau structures, K3 surfaces, and B-fields

Details Generalized Calabi-Yau structures, K3 surfaces, and B-fields Generalized Calabi-Yau structures, K3 surfaces, and B-fields

2003-06-10

arxiv.org/abs/math/0306162v2

Int.J.Math. 16 (2005) 13

Mathematics

Algebraic Geometry

24 pages. This final version of the paper, to appear in Int.J.Math., contains further comments on N=(2,2) susy, the definition

Scientific paper

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.

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