Special Kähler metrics on complex line bundles and the geometry of $K3$-surfaces

Ya. V. Bazaikin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We construct metrics with the holonomy group $SU(2)$ on the tangent bundles of weighted complex projective lines. We give a geometric description of a neighborhood of the moduli space of special Kähler metrics on a $K3$-surface.

Keywords: special Kähler manifold, $K3$-surface.

UDC: 514.764.22

Received: 10.11.2004

 English version: Siberian Mathematical Journal, 2005, 46:6, 995–1004

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