The Maximal Number of Quotient Singularities on Surfaces with Given Numerical Invariants.
The Milnor number of functions on singular hypersurfaces
The behaviour of a holomorphic map germ at a critical point has always been an important part of the singularity theory. It is generally known (cf. [5]) that we can associate an integer invariant - called the multiplicity - to each isolated critical point of a holomorphic function of many variables. Several years later it was noticed that similar invariants exist for function germs defined on isolated hypersurface singularities (see [1]). The present paper aims to show a simple approach to critical...
The Modell-Weil groups of unirational quasi-elliptic surfaces in characteristic 3.
The modularity of the Barth-Nieto quintic and its relatives.
The moduli and the global period mapping of surfaces with : a counterexample to the global Torelli problem
The Moduli of Weierstrass Fibriations Over P1 .
The Moduli Space of (3,3,3) Trilinear forms.
The Moduli Space of 3-Folds with K = 0 may Nevertheless be Irreducible.
The moduli space of special lagrangian submanifolds
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...).