Related papers: Lectures on complements on log surfaces
The note complements topological aspects of the theory of chiral algebras.
In this paper the log surfaces without $\QQ$-complement are classified. In particular, they are non-rational always. This result takes off the restriction in the theory of complements and allows one to apply it in the most wide class of log…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
This is a survey on the recent fundamental paper by V.V. Shokurov on the existence of log flips.
More strong version of the main inductive theorem about the complements on surfaces is proved and the models of exceptional log del Pezzo surfaces with $\delta=0$ are constructed
We prove a conjecture due to V.V. Shokurov on the boundedness of $\epsilon$-log canonical complements on surfaces. As an application we give a new proof to the boundedness of weak log Fano surfaces.
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
The purpose of this paper is to lay the foundations for the theory of higher rank b-divisorial algebras of Shokurov type. We develop techniques to deal with such objects and propose two natural conjectures regarding Shokurov algebras and…
This is a series of lecture notes explaining topos theory and its application in physics.
This paper is an announcement of the minimal model theory for log surfaces in all characteristics and contains some related results including a simplified proof of the Artin-Keel contraction theorem in the surface case.
This is an introduction to topology of complement to plane curves and hypersurfaces in the projective space and is based on the lectures given in Lumini in February and in ICTP (Trieste) in August of 2005. We discuss key problems concerning…
The goal of these notes is to give a self-contained account of the representation theory of $GL_2$ and $SL_2$ over a finite field, and to give some indication of how the theory works for $GL_n$ over a finite field.
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
The paper reviews recent developments in the study of Alexander invariants of quasi-projective manifolds using methods of singularity theory. Several results in topology of the complements to singular plane curves and hypersurfaces in…
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
The aim of this paper is to clarify and generalize techniques of works alg-geom/9711024 (see also math.AG/9810097 and math.AG/9901004). Roughly speaking, we prove that for local Fano contractions the existence of complements can be reduced…
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…