Counting Lines on Quartic Surfaces

We prove the sharp bound of at most 64 lines on complex projective quartic surfaces (resp. affine quartics) that are not ruled by lines. We study configurations of lines on certain non-K3 surfaces of degree four and give various examples of singular quartics with many lines

Non-factorial nodal complete intersection threefolds

We give a bound on the minimal number of singularities of a nodal projective complete intersection threefold which contains a smooth complete intersection surface that is not a Cartier divisor

24 rational curves on K3 surfaces

Given d in IN, we prove that all smooth K3 surfaces (over any field of characteristic p other than 2,3) of degree greater than 84d^2 contain at most 24 rational curves of degree at most d. In the exceptional characteristics, the same bounds hold for non-unirational K3 surfaces, and we develop analogous results in the unirational case. For d at least 3, we also construct K3 surfaces of any degree greater than 4d(d+1) with 24 rational curves of degree exactly d, thus attaining the above bounds.Comment: v2: 20 pages; effective bounds for the polarization incorporated; exposition adjuste

On the geometry of the Coble-Dolgachev sextic

In this paper, we study the intersection of the Coble-Dolgachev sextic with special projective spaces. Let us recall that the Coble-Dolgachev sextic C_6 is the branch divisor of a double cover map. The adjunction of divisors is an involution of Pic^1(X) that lifts to a non-trivial involution. The fixed locus Fix(τ) is the disjoint union of two projective spaces P^4 and P^3

Convergence of holomorphic chains

We endow the module of analytic p-chains with the structure of a second-countable metrizable topological space