Bert van Geemen

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We study a proposal of D'Hoker and Phong for the chiral superstring measure for genus three. A minor modification of the constraints they impose on certain Siegel modular forms leads to a unique solution. We reduce the problem of finding these modular forms, which depend on an even spin structure, to finding a modular form of weight 8 on a certain subgroup(More)
We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) in-volution on a K3 surface. We parametrize the eleven dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components. We conclude with some remarks on Morrison-Nikulin(More)
We complete the proof of the fact that the moduli space of rank two bundles with trivial determinant embeds into the linear system of divisors on P ic g−1 C which are linearly equivalent to 2Θ. The embedded tangent space at a semi-stable non-stable bundle ξ ⊕ ξ −1 , where ξ is a degree zero line bundle, is shown to consist of those divisors in |2Θ| which(More)