Deformations of Scalar-Flat Anti-Self-Dual metrics and Quotients of Enriques Surfaces

Details Deformations of Scalar-Flat Anti-Self-Dual metrics and Quotients of Enriques Surfaces Deformations of Scalar-Flat Anti-Self-Dual metrics and Quotients of Enriques Surfaces

2006-11-25

arxiv.org/abs/math/0611772v2

Proceedings of the 13th G\"okova geometry-topology conference, G\"okova, Turkey, May 28-June 2, 2006. Cambridge, MA: Internati

Mathematics

Differential Geometry

12 pages. Extensions and corrections are done according to the referee report. To be published in the Turkish Journal of Mathe

Scientific paper

In this article, we prove that a quotient of a $K3$ surface by a free ${\mbb Z}_2\oplus{\mbb Z}_2$ action does not admit any metric of positive scalar curvature. This shows that the scalar flat anti self-dual metrics (SF-ASD) on this manifold can not be obtained from a family of metrics for which the scalar curvature changes sign, contrary to the previously known constructions of this kind of metrics on manifolds of $b^+=0$

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