Related papers: Algebraic Surfaces and their Moduli Spaces: Real, …
We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of…
The article is a slightly extended version of the talk, with the same title, which I gave at the Kinosaki Symposium on Algebraic Geometry in October 2011, and dealing with the classification of complex projective surfaces of general type…
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…
We study the birational geometry of some moduli spaces of abelian varieties with extra structure: in particular, with a symmetric theta structure and an odd theta characteristic. For a $(d_1,d_2)$-polarized abelian surface, we show how the…
We study on a new kind of surface covered by translation and factorable (TF-type) surfaces in the three dimensional Euclidean space. We consider I and III Laplace-Beltrami operator surfaces of a TF-type surface. Then we obtain degrees and…
We study framed translation surfaces corresponding to meromorphic differentials on compact Riemann surfaces, for which a horizontal separatrix is marked for each pole or zero. Such geometric structures naturally appear when studying flat…
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…
The moduli space of abelian surfaces with polarisation of type (1,t) and a bilevel structure is of general type if t is odd and at least 17.
We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.
In this paper, we study the moduli space of $1|2$-dimensional complex associative algebras, which is also the moduli space of codifferentials on the tensor coalgebra of a $2|1$-dimensional complex space. We construct the moduli space by…
This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal…
The volumes of strata of Abelian or quadratic differentials play an important role in the study of dynamics on flat surfaces, related to dynamics in polygonal billiards. This article reviews all known ways to compute volumes in the…
A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…
Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust…
This paper develops some of the methods of the "Italian School" of algebraic geometry in the context of infinitesimals. The results of this paper have no claim to originality, they can be found in Severi, we have only made the arguments…
We compute a large number of moduli spaces of stable bundles on a general algebraic elliptic surface using a new class of Fourier-Mukai type transforms.
This is a survey paper: we discuss certain recent results, with some improvements. It will appear in the S. Cruz proceedings.
We discuss the role played by logarithmic structures in the theory of moduli.
In this revised version, we add some expository material and references and make some minor corrections.
We study the moduli space of $J$-holomorphic subvarieties in a $4$-dimensional symplectic manifold. For an arbitrary tamed almost complex structure, we show that the moduli space of a sphere class is formed by a family of linear system…