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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)
The endomorphism algebra of a K3 type Hodge structure is a totally real field or a CM field. In this paper we give a low brow introduction to the case of a totally real field. We give existence results for the Hodge structures, for their polarizations and for certain K3 surfaces. We consider the Kuga Satake variety of these Hodge structures and we discuss… (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)
To a Hodge structure V of weight k with CM by a eld K we associate Hodge structures V ?n=2 of weight k + n for n positive and, under certain circumstances, also for n negative. We show that thesèhalf twists' come up naturally in the Kuga-Satake varieties of weight two Hodge structures with CM by an imaginary quadratic eld.
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)