The field of definition for dynamical systems on
The Formal Hodge Filtration.
The fundamental group for the complement of Cayley's singularities.
The fundamental group of a Galois cover of .
The Fundamental Group of the Complement of a Union of Complex Hyperplanes.
The fundamental group of the complement of a union of complex hyperplanes: correction.
The Fundamental Group-Scheme of an Abelian Variety.
The Galois structure of S-units
The Hilbert Modular Surface of a Real Quadratic Field.
The Kähler cone on Calabi-Yau threefolds.
The Kähler cone on Calabi-Yau threefolds (Erratum).
The last coefficient of the Samuel polynomial
The last coefficient of the Samuel polynomial
The Maximal Number of Quotient Singularities on Surfaces with Given Numerical Invariants.
The Maximal Rank Conjecture for Non-Special Curves in Ipn.
The membership problem for polynomial ideals in terms of residue currents
We find a relation between the vanishing of a globally defined residue current on and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther’s theorem, for which we also obtain a generalization. Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.
The Milnor Number and Deformations of Complex Curve Singularities.
The minimal freee resolution of the homogeneous ideal of s general points in P4.
The monodromy conjecture for zeta functions associated to ideals in dimension two
The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot. However in full generality it is proven only for zeta functions associated to polynomials in two variables.In this article we work with zeta functions associated to an ideal. First we work in arbitrary dimension and obtain a formula (like the one of A’Campo) to compute the “Verdier monodromy” eigenvalues associated to an...
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).