Related papers: Algebraic surfaces and Seiberg-Witten invariants

: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…

We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.

This is a version of the author's diploma thesis written at the University of Cologne in 2002/03. The topic is the construction of Seiberg-Witten invariants of closed 3-manifolds. In analogy to the four dimensional case, the structure of…

Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is…

Memoir on the Sigma invariants and their applications, version 2

We collect in this note some observations about original Welschinger invariants of real symplectic fourfolds. None of their proofs is difficult, nevertheless these remarks do not seem to have been made before. Our main result is that when…

In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation…

The purpose of this note is to give a short, selfcontained proof of the following result: A complex surface which is diffeomeorphic to a rational surface is rational.

The results of this paper are outdated. Finer versions of them will appear elsewhere.

We give an introduction to the study of algebraic hypersurfaces, focusing on the problem of when two hypersurfaces are isomorphic or close to being isomorphic. Working with hypersurfaces and emphasizing examples makes it possible to discuss…

The following is an extended version of a talk given at the Kinosaki Symposium on Algebraic Geometry in October 2011. The aim is to give an overview of product-quotient surfaces, the results that have been proven so far in collaboration…

This article provides a summary of arXiv:1701.08899 and arXiv:1701.08902 where the authors studied the enumerative geometry of nested Hilbert schemes of points and curves on algebraic surfaces and their connections to threefold theories,…

In the article it was shown the convergence of special integral of two dimensional Terry's problem. Main tools of the article are an investigation of real algebraic varieties and estimations of areas of algebraic surfaces.

We construct explicit equations of Cartwright-Steger and related surfaces.

In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.

Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

Recent developments in Seiberg-Witten theory and relations with Complex Geometry.

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…

We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we…