Technique de descente et théorèmes d'existence en géométrie algébriques. II. Le théorème d'existence en théorie formelle des modules
Tensor product theorem for Hitchin pairs – An algebraic approach
We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields of characteristic zero and characteristic , with satisfying some natural bounds. We also prove the corresponding theorem for polystable Hitchin pairs.
The algebraic Bethe Ansatz and vacuum vectors.
The ampleness of the theta divisor on the compactified jacobian of a proper and integral curve
The Atiyah extension of a Lie algebra deformation.
The automorphism group of
The paper studies fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov’s description we are able to prove that the only such morphisms are forgetful maps. This allows us to show that the automorphism group of is the permutation group on elements as soon as .
The automorphism group of the moduli space of semi stable vector bundles.
The Behaviour of the Plurigenera of Surfaces Under Algebraic Smooth Deformations.
The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface.
The Betti numbers of the moduli space of stable sheaves of rank2 on P2.
The Chern Classes of the Stable Rank 3 Vector Bundles on IP3.
The Chow ring of the stack of cyclic covers of the projective line
In this paper we compute the integral Chow ring of the stack of smooth uniform cyclic covers of the projective line and we give explicit generators.
The cohomology rings of moduli stacks of principal bundles over curves.
The concept of (ν)-equivalence in algebraic deformation theory
The cylinder homomorphism associated to quintic fourfolds
The decomposition and specialization of algebraic families of vector bundles
The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity
Let X be a quotient surface singularity, and define as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture...
The deformation theory of representations of fundamental groups of compact Kähler manifolds
The geometry of Calogero-Moser systems
We give a geometric construction of the phase space of the elliptic Calogero-Moser system for arbitrary root systems, as a space of Weyl invariant pairs (bundles, Higgs fields) on the -th power of the elliptic curve, where is the rank of the root system. The Poisson structure and the Hamiltonians of the integrable system are given natural constructions. We also exhibit a curious duality between the spectral varieties for the system associated to a root system, and the Lagrangian varieties for...
The Group of Automorphisms of the Modular Function Field.