Related papers: Algebraic surfaces and Seiberg-Witten invariants
In preparing the paper "Some extensions of Hilbert-Kunz multiplicity", we had occasion to perform an intricate set of computations pertaining to a single illustrative example. In the end, we have decided not to include the computations in…
The article surveys the known results and conjectures about the analytic properties of dispersion relations and Fermi surfaces for periodic equations of mathematical physics and their spectral incarnations.
An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.
The paper presents an analog of the old result by the author and V. Voevodsky, according to which a Riemann surface admits a conformal structure, defined by an equilateral triangulation, if and only if the corresponding algebraic curve can…
A new invariant, the Pontrjagin-Viro form, of algebraic surfaces is introduced and studied. It is related to various Rokhlin-Guillou-Marin forms and generalizes Mikhalkin's complex separation. The form is calculated for all real Enriques…
This paper generalizes the bordered-algebraic knot invariant introduced in an earlier paper, giving an invariant now with more algebraic structure. It also introduces signs to define these invariants with integral coefficients. We describe…
In this paper we give a geometrically invariant spinorial representation of surfaces in four-dimensional space forms. In the Euclidean space, we obtain a representation formula which generalizes the Weierstrass representation formula of…
We introduce general weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles and describe their basic properties. In particular, we prove that all these algebras, except the singular disc, triangle,…
This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of…
In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…
We construct Ionel-Parker's proposed refinement of the standard relative Gromov-Witten invariants in terms of abelian covers of the symplectic divisor and discuss in what sense it gives rise to invariants. We use it to obtain some vanishing…
We collect some classical results on the versal families of ordinary compact Riemann surfaces needed in `Versal Families of Compact Super Riemann Surfaces'.
In this paper we construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in…
This paper extends two recent improvements in the Hilbert space setting of the well-known Katznelson-Tzafriri theorem by establishing both a version of the result valid for bounded representations of a large class of abelian semigroups and…
This paper has been withdrawn by the author
We introduce defects, with internal gauge symmetries, on a knot and Seifert surface to a knot into the combinatorial construction of finite gauge-group Dijkgraaf-Witten theory. The appropriate initial data for the construction are certain…
Integrals related to the surface area of arbitrary ellipsoids are derived, evaluated, and compared with each other and existing integrals found in the literature. We clarify the literature on the ellipsoid area problem, which dates back to…
We develop a direct and elementary (calculus-free) exposition of the famous cubic surface of revolution x^3+y^3+z^3-3xyz=1.12 pages. We have added a second elementary proof that the surface is of revolution.
Based on invariant algebras, we introduce representations$^{6-th}$ of Lie algebras and representations$^{< 4-th>}$ of Leibniz algebras, give the extended P-B-W Theorems in the context of the new representations of Lie algebras and Leibniz…
An increasingly important area of interest for mathematicians is the study of Abelian differentials. This growing interest can be attributed to the interdisciplinary role this subject plays in modern mathematics, as various problems of…