Related papers: Algebraic surfaces and Seiberg-Witten invariants
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
We introduce the notions of mixed resolutions and simplicial sections, and prove a theorem relating them. This result is used (in another paper) to study deformation quantization in algebraic geometry.
We introduce a geometric refinement of Gromov-Witten invariants for $\mathbb P^1$-bundles relative to the natural fiberwise boundary structure. We call these refined invariant correlated Gromov-Witten invariants. Furthermore, we prove a…
For a complex projective manifold Gromov-Witten invariants can be constructed either algebraically or symplectically. Using the versions of Gromov-Witten theory by Behrend and Fantechi on the algebraic side and by the author on the…
In this paper, we derive new adjunction inequalities for embedded surfaces with non-negative self-intersection number in four-manifolds. These formulas are proved by using relations between Seiberg-Witten invariants which are induced from…
We determine the Krull-Gabriel dimension of weighted surface algebras, a class of algebras which recently appeared in the context of classification of tame symmetric periodic algebras of non-polynomial growth. Moreover, we consider…
This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.
The original version of this paper has been withdrawn by the authors and merged with the revised version of astro-ph/9702014.
We extend all cohomological invariants of similarity classes of quadratic forms to anti-hermitian forms over a quaternion algebra. This uses the fact that such invariants can be lifted to Witt invariants, which can be described as…
In this paper we construct new derived invariants with integral coefficients using the theory of motifs, and give several applications. Specifically, we obtain the following results: For complex algebraic surfaces, we prove that certain…
This version has been withdrawn. The new and final version is on ArXiv 1103.4878
We will announce two theorems. The first theorem will classify all topological types of degenerate fibers appearing in one-parameter families of Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The second theorem…
This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low…
The paper is a colloquial-style discussion of invariants of algebraic surfaces analogous to the Donaldson polynomials, arising from moduli spaces of ``jumping'' Yang--Mills instantons, or moduli spaces of jumping vector bundles. The…
Additive deformations of bialgebras in the sense of J. Wirth, i.e. deformations of the multiplication map fulfilling a certain compatibility condition w.r.t. the coalgebra structure, can be generalized to braided bialgebras. The theorems…
We survey on algebraically elliptic varieties in the sense of Gromov.
Talk presented by the second author at the Inaugural Coference of the Asia Pacific Center for Theoretical Physics, Seoul, June 1996. The purpose of this note is to give a resume of the Seiberg-Witten theory in the simplest possible…
In this paper, we explore the structure of the Hitchin map for higher dimensional varieties with emphasis on the case of algebraic surfaces.
All reduced descendent Gromov-Witten invariants of $K3$ and abelian surfaces in primitive curve classes can be calculated by the methods of \cite{BOPY,MPT}. To handle the imprimitive curve classes, a multiple cover formula was conjectured…
This is a survey of known algorithms in algebraic topology with a focus on finite simplicial complexes and, in particular, simplicial manifolds. Wherever possible an elementary approach is chosen. This way the text may also serve as a…