In these notes we construct a quantization functor, associating a Hilbert space H(V ) to a finite dimensional symplectic vector space V over a finite field Fq. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp (V ). The main technical result is a proof of a stronger form of the Stonevon Neumann theorem for the Heisenberg group over Fq. Our result an...

Let G be a finite group, Λ an absolutely irreducible Z[G]-module and w a weight of Λ. To any Galois covering with group G we associate two correspondences, the Schur and the Kanev correspondence. We work out their relation and compute their invariants. Using this, we give some new examples of Prym-Tyurin varieties.

In this paper, we study the bicanonical pencil of a Godeaux surface and of a determinantal Barlow surface. This study gives a simple proof for the unobstructedness of deformations of a determinantal Barlow surface. Then we compute the number of hyperelliptic curves in the bicanonical pencil of a determinantal Barlow surface via classical Prym theory.

We introduce endomorphisms of special jacobians and show that they satisfy polynomial equations with all integer roots which we compute. The eigen-abelian varieties for these endomorphisms are generalizations of Prym-Tyurin varieties and naturally contain special curves representing cohomology classes which are not expected to be represented by curves in generic abelian varieties.

n≥0 Γ(nKMg). Mg has been proven to be of general type for g ≥ 22 [EH,Fa,HaMu]. In particular in this case the finite generation of the canonical ring implies that the canonical model is birational to Mg. Recent progress has been made in this area. For example [BCHM] have proved the existence of canonical models in the case of smooth projective varieties of general type. A somewhat easier proble...

Let $f\colon S'\longrightarrow S$ be a cyclic branched covering of smooth projective surfaces over $\mathbb{C}$ whose branch locus $\Delta\subset is ample divisor. Pick very complete linear system $|\mathcal{H}|$ on $S$, such that the polarized surface $(S, |\mathcal{H}|)$ not scroll nor has rational hyperplane sections. For general member $[C]\in|\mathcal{H}|$ consider $\mu_{n}$-equivariant is...