Search: MSC category 14J10
( Families, moduli, classification: algebraic theory )
1. CMB Online first
||Projective plane bundles over an elliptic curve|
We calculate the dimension of cohomology groups for
the holomorphic tangent bundles of each isomorphism
class of the projective plane bundle over an elliptic curve.
As an application, we construct the families
of projective plane bundles, and prove that the families
are effectively parametrized and complete.
Keywords:projective plane bundle, vector bundle, elliptic curve, deformation, Kodaira-Spencer map
Categories:14J10, 14J30, 14D15
2. CMB 2009 (vol 52 pp. 493)
||A One-Dimensional Family of $K3$ Surfaces with a $\Z_4$ Action |
The minimal resolution of the degree four cyclic cover of the plane
branched along a GIT stable quartic is a $K3$ surface with a non
symplectic action of $\Z_4$. In this paper
we study the geometry of the one-dimensional family of $K3$ surfaces
associated to the locus of plane quartics with five nodes.
Keywords:genus three curves, $K3$ surfaces
Categories:14J28, 14J50, 14J10