The Intersection of Four Quadrics in IP6, Abelian Surfaces and their Moduli.
The Kodaira dimension of certain moduli spaces of abelian surfaces
The Kodaira dimension of the moduli space of Prym varieties
We study the enumerative geometry of the moduli space of Prym varieties of dimension . Our main result is that the compactication of is of general type as soon as and is different from 15. We achieve this by computing the class of two types of cycles on : one defined in terms of Koszul cohomology of Prym curves, the other defined in terms of Raynaud theta divisors associated to certain vector bundles on curves. We formulate a Prym–Green conjecture on syzygies of Prym-canonical curves....
The K.P. Hypothesis for decomposable Abelian Varieties.
The moduli space of curves of genus two covering elliptic curves.
The moduli spaces of polarized abelian varieties.
The Mordell conjecture revisited
The Néron Fiber of Abelian Varieties with Potential Good Reduction.
The Neron model for families of intermediate jacobians acquiring “algebraic” singularities
The optimality of the Bounded Height Conjecture
In this article we show that the Bounded Height Conjecture is optimal in the sense that, if is an irreducible subvariety with empty deprived set in a power of an elliptic curve, then every open subset of does not have bounded height. The Bounded Height Conjecture is known to hold. We also present some examples and remarks.
The -adic finite Fourier transform and theta functions.
The -rank stratification of Artin-Schreier curves
We study a moduli space for Artin-Schreier curves of genus over an algebraically closed field of characteristic . We study the stratification of by -rank into strata of Artin-Schreier curves of genus with -rank exactly . We enumerate the irreducible components of and find their dimensions. As an application, when , we prove that every irreducible component of the moduli space of hyperelliptic -curves with genus and -rank has dimension . We also determine all pairs for...
The periods of abelian varieties with complex multiplication and the spectral values of certain zeta functions
The Picard group of a scheme over an Artin ring
The polynomial and elliptic curves of conductor 11
The principal degenerations of abelian surfaces and their polarisations.
The Schottky-Jung theorem for Mumford curves
The Schottky-Jung proportionality theorem, from which the Schottky relation for theta functions follows, is proved for Mumford curves, i.e. curves defined over a non-archimedean valued field which are parameterized by a Schottky group.
The Spectrum of Jacobi Matrices.
The structure of Gauss-like maps
The structure of proper rigid groups.