The Moduli spaces of Rank 2 Stable Vector Bundles over Veronesean surfaces.
The monodromy of a series of hypersurface singularities.
The Mukai conjecture for log Fano manifolds
For a log Fano manifold (X,D) with D ≠ 0 and of the log Fano pseudoindex ≥2, we prove that the restriction homomorphism Pic(X) → Pic(D 1) of Picard groups is injective for any irreducible component D 1 ⊂ D. The strategy of our proof is to run a certain minimal model program and is similar to Casagrande’s argument. As a corollary, we prove that the Mukai conjecture (resp. the generalized Mukai conjecture) implies the log Mukai conjecture (resp. the log generalized Mukai conjecture).
The multiple conical surfaces.
The Nash conjecture for threefolds.
The Nash problem of arcs and the rational double points
This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points ().
The non rationality of the generic Enriques' threefold
The non-existence of a smooth sectionally non-special surface of degree 11 and sectional genus 8 in the projective fourspace.
The Normal Bundle of a Curve on a Quadric.
The Normalizer of the level (2,2)-Heisenberg Group.
The Number of Rational Quartics on Calabi-Yau Hypersurfaces in Weighted Projective Space P (2,1...).
The number of reducible hypersurfaces in a pencil.
The number of reducible hypersurfaces in a pencil (Erratum).
The Number of the Minimal Models for a 3- Fold of General Type is Finite.
The Number of Twisted Cubic Curves on the General Quintic Threefold.
The number of vertices of a Fano polytope
Let be a Gorenstein, -factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number of vertices of a simplicial reflexive polytope.
The Picard group of a primary Kodaira surface.
The Picard group of Siegel modular threefolds.
The plurigenera of Gorenstein surface singularities.
The principal degenerations of abelian surfaces and their polarisations.