2 00 6 Monoid hypersurfaces

N ov 2 00 6 INTEGRAL POINTS ON CUBIC HYPERSURFACES

1 F eb 2 00 6 Homogeneous Levi degenerate CR - manifolds in dimension 5

Levi nondegenerate real-analytic hypersurfaces M ⊂ ƒ are well understood due to the seminal results of Tanaka [17] and Chern-Moser[5], where a complete set of local invariants for M has been defined. At the other extreme are those hypersurfaces which are locally CR-equivalent to a product M ׃, (take the real hyperplanes inƒ as a simple example). In-between there is a huge and much less underst...

1 9 M ay 2 00 6 DEGENERATE REAL HYPERSURFACES IN C 2 WITH FEW AUTOMORPHISMS

We introduce new biholomorphic invariants for real-analytic hypersurfaces in C and show how they can be used to show that a hypersurface possesses few automorphisms. We give conditions, in terms of the new invariants, guaranteeing that the stability group is finite, and give (sharp) bounds on the cardinality of the stability group in this case. We also give a sufficient condition for the stabil...

0 A ug 2 00 6 Hypergeometric series and Hodge cycles of four dimensional cubic hypersurfaces

In this article we find connections between the values of Gauss hypergeometric functions and the dimension of the vector space of Hodge cycles of four dimensional cubic hypersurfaces. Since the Hodge conjecture is well-known for those varieties we calculate values of Hypergeometric series on certain CM points. Our methods is based on the calculation of the Picard-Fuchs equations in higher dimen...

N ov 2 00 5 Factorial hypersurfaces in P 4 with nodes

We prove that for n = 5, 6, 7 a nodal hypersurface of degree n in P is factorial if it has at most (n− 1) − 1 nodes.