A Simple Proof of the Subjectivity of the Period Map of K3 Surfaces.
A simple solution of Hilbert's fourteenth problem in dimension five
We give a short proof of a counterexample (due to Daigle and Freudenburg) to Hilbert's fourteenth problem in dimension five.
A simpler proof of the Gieseker-Petri Theorem on special divisors.
A simpler proof of toroidalization of morphisms from 3-folds to surfaces
We give a simpler and more conceptual proof of toroidalization of morphisms of 3-folds to surfaces, over an algebraically closed field of characteristic zero. A toroidalization is obtained by performing sequences of blow ups of nonsingular subvarieties above the domain and range, to make a morphism toroidal. The original proof of toroidalization of morphisms of 3-folds to surfaces is much more complicated.
A simplified proof of desingularization and applications.
This paper contains a short and simplified proof of desingularization over fields of characteristic zero, together with various applications to other problems in algebraic geometry (among others, the study of the behavior of desingularization of families of embedded schemes, and a formulation of desingularization which is stronger than Hironaka's). Our proof avoids the use of the Hilbert-Samuel function and Hironaka's notion of normal flatness: First we define a procedure for principalization of...
A simply connected surface of general type with pg = 0.
A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices
A singular Riemann-Roch for Hirzebruch characteristics
A Six Exponentials Theorem in Finite Characteristic.
A Smooth Four-Dimensional G-Hilbert Scheme
2000 Mathematics Subject Classification: 14C05, 14L30, 14E15, 14J35.When the cyclic group G of order 15 acts with some specific weights on affine four-dimensional space, the G-Hilbert scheme is a crepant resolution of the quotient A^4 / G. We give an explicit description of this resolution using G-graphs.
A souped-up version of Pardini's theorem and its application to funny curves
A special case of the Garnier system, -polarized abelian surfaces and their moduli
A spectral sequence for de Rham cohomology
A splitting criterion for rank 2 vector bundles on hypersurfaces in .
A splitting principle and the algebraic K-theory of some homogeneous varieties
A splitting theorem for the Kupka component of a foliation of . Addendum to a paper by O. Calvo-Andrade and N. Soares
Here we show that a Kupka component of a codimension 1 singular foliation of with not a square is a complete intersection. The result implies the existence of a meromorphic first integral of .
A splitting theorem for the Kupka component of a foliation of . Addendum to an addendum to a paper by Calvo-Andrade and Soares
Here we show that a Kupka component of a codimension 1 singular foliation of is a complete intersection. The result implies the existence of a meromorphic first integral of . The result was previously known if was assumed to be not a square.
A standard basis approach to syzygies of canonical curves.
A Stratification of the Hilbert Scheme of Points in the Projective Plane.
A Study of Hasse-Witt Matrices by Local Methods.