Local fundamental groups of surface singularities in characteristic p.
Local geometry of smooth curves passing through rational double points.
Localisation formelle et groupe de Picard
Soient un espace analytique affinoïde réduit sur un corps complet pour une valeur absolue non archimédienne, sa réduction canonique et un point de la variété algébrique affine . Ce travail décrit la singularité du point à l’aide d’objets associés à l’espace : la localisation formelle qui est une -algèbre noethérienne de spectre maximal et dont la réduction est ; un complété formel qui est une -algèbre noethérienne dont la réduction est . Les résultats essentiels sont obtenus...
Matrix factorizations and singularity categories for stacks
We study matrix factorizations of a potential W which is a section of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with potential W) with the singularity category of the zero locus of W generalizing a theorem of Orlov. We use this result to construct push-forward functors for matrix factorizations with relatively proper support.
Matrix factorizations for domestic triangle singularities
Working over an algebraically closed field k of any characteristic, we determine the matrix factorizations for the-suitably graded-triangle singularities of domestic type, that is, we assume that (a,b,c) are integers at least two satisfying 1/a + 1/b + 1/c > 1. Using work by Kussin-Lenzing-Meltzer, this is achieved by determining projective covers in the Frobenius category of vector bundles on the weighted projective line of weight type (a,b,c). Equivalently, in a representation-theoretic context,...
Maximal Orders of global dimension and Krull dimension two.
Modules of finite length and -groups of surface singularities
Multiplizitäten "unendlich-ferner" Spitzen.
Natural -constellation families.
Nevanlinna Defect Relations for Singular Divisors.
Newton Polyhedra and Irreducibility.
Non-smoothable varieties.
Normal degenerations of the complex projective plane.
Normal projective degenerations of rational and ruled surfaces.
Normal surface singularities admitting contracting automorphisms
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting automorphism.
Note sur la théorie de surfaces réciproques
Nouvelles surfaces à noeuds dans IP3.
On Auslander Modules of Normal Surface Singularities.
On blowing down projective spaces in singular varieties.
On Enriques Surfaces in Characteristic p. II.