A Class of Indecomposable Algebraic Vector Bundles.
A class of n-bundles on Gr (k, n).
A class of non-rational surface singularities with bijective Nash map
Let be a germ of complex analytic normal surface. On its minimal resolution, we consider the reduced exceptional divisor and its irreducible components , . The Nash map associates to each irreducible component of the space of arcs through on the unique component of cut by the strict transform of the generic arc in . Nash proved its injectivity and asked if it was bijective. As a particular case of our main theorem, we prove that this is the case if for any .
A classical complex analyst encounters a post-modern mathematical object.
A Classical Diophantine Problem and Modular Forms of Weight 3/2.
A classification of reductive linear groups.
A classification of strictly pseudoconcave homogeneous manifolds
A classification of the nilpotent triangular matrices
A classification of toric varieties with few generators.
A classification theorem on Fano bundles
In this paper we classify rank two Fano bundles on Fano manifolds satisfying . The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization , that allows us to obtain the cohomological invariants of and . As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.
A Cohomological Characterization of IPn.
A combinatorial construction of sets with good quotients by an action of a reductive group
The aim of this paper is to construct open sets with good quotients by an action of a reductive group starting with a given family of sets with good quotients. In particular, in the case of a smooth projective variety X with Pic(X) = 𝒵, we show that all open sets with good quotients that embed in a toric variety can be obtained from the family of open sets with projective good quotients. Our method applies in particular to the case of Grassmannians.
A comparison of deformations and geometric study of varieties of associative algebras.
A comparison of elliptic units in certain prime power conductor cases
The aim of this paper is to compare two modules of elliptic units, which arise in the study of elliptic curves E over quadratic imaginary fields K with complex multiplication by , good ordinary reduction above a split prime p and prime power conductor (over K). One of the modules is a special case of those modules of elliptic units studied by K. Rubin in his paper [Invent. Math. 103 (1991)] on the two-variable main conjecture (without p-adic L-functions), and the other module is a smaller one,...
A Comparison Theorem.
A computation of invariants of a rational self-map
I prove the algebraic stability and compute the dynamical degrees of C. Voisin’s rational self-map of the variety of lines on a cubic fourfold.
A computer aided approach to codimension 2 subvarities of Pn, n ... 6.
A computer algebra solution to a problem in finite groups.
We report on a partial solution of the conjecture that the class of finite solvable groups can be characterised by 2-variable identities. The proof requires pieces from number theory, algebraic geometry, singularity theory and computer algebra. The computations were carried out using the computer algebra system SINGULAR.
A concept of Bernoulli numbers in algebraic function fields.
A Concept of Bernoulli Numbers in Algebraic Function Fields (II).