Cohomology of Fixed Point Sets and Deformation of Algebras.
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.
Deformation von Cohen-Macaulay Algebren.
Deformations of border bases
Deformations of free and linear free divisors
We study deformations of free and linear free divisors. We introduce a complex similar to the de Rham complex whose cohomology calculates the deformation spaces. This cohomology turns out to be zero for all reductive linear free divisors and to be constructible for Koszul free divisors and weighted homogeneous free divisors.
Deformations of graded algebras.
Deforming syzygies of liftable modules and generalised Knörrer functors
Maps between deformation functors of modules are given which generalise the maps induced by the Knörrer functors. These maps become isomorphisms after introducing certain equations in the target functor restricting the Zariski tangent space. Explicit examples are given on how the isomorphisms extend results about deformation theory and classification of MCM modules to higher dimensions.
Dénombrement des types de K-homotopie. Théorie de la déformation
Derivations and Deformations of Artinian Algebras
Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves
Eindimensionale fast-vollständige Durchschnitte sind nicht starr.
Ergänzung und Berichtigung zu : Die Zahl der Spitzen und die Jacobi-Algebra einer isolierten Hyperflächensingularität.
Flache T1-Stabilität in der Stratifizierung Verseller Entfaltungen.
Formal deformation of curves with group scheme action
We study equivariant deformations of singular curves with an action of a finite flat group scheme, using a simplified version of Illusie's equivariant cotangent complex. We apply these methods in a special case which is relevant for the study of the stable reduction of three point covers.
Fragmented deformations of primitive multiple curves
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization...
Generic determinantal schemes and the smoothability of determinantal schemes of codimension 2.
Géométrie des points épais
Higher Kodaira-Spencer classes.
Lie description of higher obstructions to deforming submanifolds
To every morphism of differential graded Lie algebras we associate a functors of artin rings whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of . Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanifold of a Kähler manifold is annihilated by the semiregularity map.