On Singular Complex Surfaces with Negative Canonical Bundle, with Applications to Singular Compactifications of C2 and to 3-Dimensional Rational Singularities.
On singular complex surfaces with vanishing geometric genus, and pararational singularities
On singularities arising from the contraction of the minimal section a a ruled surface.
On Singularities in the Classification Theory of Algebraic Varieties.
On smooth curves passing through rational surface singularities.
On smooth surfaces in Gr(1, P3) with a fundamental curve.
On Some Arithmetic Problems Related to the Hodge Cycles on the Fermat Varieties.
On Some Arithmetic Problems Related to the Hodge Cycles on the Fermat Varieties (Erratum).
On some components of moduli space of surfaces of general type
On some numerical properties of Fano varieties
This is the text of a talk given at the XVII Convegno dellUnione Matematica Italiana held at Milano, September 8-13, 2003. I would like to thank Angelo Lopez and Ciro Ciliberto for the kind invitation to the conference. I survey some numerical conjectures and theorems concerning relations between the index, the pseudo-index and the Picard number of a Fano variety. The results I refer to are contained in the paper [3], wrote in collaboration with Bonavero, Debarre and Druel.
On some special Fano manifolds.
On stable conjugacy of finite subgroups of the plane Cremona group, I
We discuss the problem of stable conjugacy of finite subgroups of Cremona groups. We compute the stable birational invariant H 1(G, Pic(X)) for cyclic groups of prime order.
On sums of algebraic surfaces.
On Surfaces of Class VII0 with Curves.
On surfaces of general type with pg = q = 1, K2 = 3.
The moduli space M of surfaces of general type with pg = q = 1, K2 = g = 3 (where g is the genus of the Albanese fibration) was constructed by Catanese and Ciliberto in [14]. In this paper we characterize the subvariety M2 ⊂ M corresponding to surfaces containing a genus 2 pencil, and moreover we show that there exists a non-empty, dense subset M0 ⊂ M which parametrizes isomorphism classes of surfaces with birational bicanonical map.
On surfaces with p = q = 1 and non-ruled bicanonical involution
This paper classifies surfaces of general type with having an involution such that has non-negative Kodaira dimension and that the bicanonical map of factors through the double cover induced by It is shown that is regular and either: a) the Albanese fibration of is of genus 2 or b) has no genus 2 fibration and is birational to a surface. For case a) a list of possibilities and examples are given. An example for case b) with is also constructed.
On surfaces with and non-birational bicanonical maps.
On the (-1)-curve conjecture of Friedmann and Morgan.
On the 2 and the 3-connectedness of ample divisors on a surface.
On the 2 Very Ampleness of the Adjoint Bundle.