Darstellbarkeitskriterien für analytische Funktoren
Das formale Prinzip und Modifikationen komplexer Räume.
Das Horrocks-Mumford-Bündel und das Modul-Schema für stabile 2-Vektorbündel über IP4 mit c1= -1, c2 = 4.
Das Spektrum torsionsfreier Garben I.
D'autres composantes non réduites de Hilb IP3.
de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities
We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic (as defined by Abramovich, Olsson, and Vistoli) which lift mod degenerates. We push the result to the coarse spaces of such stacks, thereby obtaining a degeneracy result for schemes which are étale locally the quotient of a smooth scheme by a finite linearly reductive group scheme.
Decomposability criterion for linear sheaves
We establish a decomposability criterion for linear sheaves on ℙn. Applying it to instanton bundles, we show, in particular, that every rank 2n instanton bundle of charge 1 on ℙn is decomposable. Moreover, we provide an example of an indecomposable instanton bundle of rank 2n − 1 and charge 1, thus showing that our criterion is sharp.
Deformation of Complete Intersections with Singularities.
Deformation of determinantal schemes
Deformation of Hilbert schemes of points on a surface
Deformation of Lie algebras and Lie algebras of deformations
Deformation of Varieties Defined by Sections in Homogeneous Vector Bundles.
Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville.
Deformation Theory (Lecture Notes)
First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section we generalize the Maurer-Cartan equation to strongly homotopy Lie algebras and prove the homotopy invariance of the moduli space of solutions of this equation. In the last...
Deformation to the normal cone, rationality and the Stückrad-Vogel cycle.
Déformations dans les schémas définis par les identités de Jacobi
Déformations de courbes avec action de groupe.
Déformations de courbes avec action de groupe II.
Déformations de courbes planes
Deformations of affine torus varieties.