相关论文: An extension of the Siegel space of complex abelia…

This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand…

We identify spaces of half-translation surfaces, equivalently complex curves with quadratic differential, with spaces of stability structures on Fukaya-type categories of punctured surfaces. This is achieved by new methods involving the…

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and…

We state conjectures on the asymptotic behavior of the volumes of moduli spaces of Abelian differentials and their Siegel-Veech constants as genus tends to infinity. We provide certain numerical evidence, describe recent advances and the…

We study moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras. The resulting symplectic manifolds are closely related with Poisson-Lie groups and their algebraic structure…

We shall study some moduli spaces of Bridgeland's semi-stable objects on abelian surfaces and K3 surfaces with Picard number 1. Under some conditions, we show that the moduli spaces are isomorphic to the moduli spaces of Gieseker…

In the present paper, we study a new kind of anabelian phenomenon concerning the smooth pointed stable curves in positive characteristic. It shows that the topological structures of moduli spaces of curves can be understood from the…

This paper studies stable sheaves on abelian surfaces of Picard number one. Our main tools are semi-homogeneous sheaves and Fourier-Mukai transforms. We introduce the notion of semi-homogeneous presentation and investigate the behavior of…

We study the moduli space of Gieseker semi-stable sheaves on the complex projective plane supported on sextic curves and having Euler characteristic one. We determine locally free resolutions of length one for all such sheaves. We decompose…

We find stability conditions ([Do], [Br]) on some derived categories of differential graded modules over a graded algebra studied in [RZ], [KS]. This category arises in both derived Fukaya categories and derived categories of coherent…

We consider some classical fibre bundles furnished with almost complex structures of twistor type, deduce their integrability in some cases and study \textit{self-holomorphic} sections of a \textit{symplectic} twistor space. With these we…

We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following…

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to…

Using the modern perspective of noncommutative algebraic geometry we survey some recent progress in the theory of stability conditions and moduli spaces with applications in hyperk\"ahler geometry and classical algebraic geometry.

This paper deals with symplectic varieties which do not have symplectic resolutions. Some moduli spaces of semi-stable torsion-free sheaves on a K3 surface, and symplectic V-manifolds are such varieties. We shall prove local Torelli theorem…

We give an explicit conjectural formula for the motivic Euler characteristic of an arbitrary symplectic local system on the moduli space A_3 of principally polarized abelian threefolds. The main term of the formula is a conjectural motive…

We study the hyperbolicity of compactifications of quotients of bounded symmetric domains by arithmetic groups. We prove that, up to an \'etale cover, they are Kobayashi hyperbolic modulo the boundary. Applying our techniques to Siegel…

1) Assuming log Minimal Model Conjecture, we give a construction of a complete moduli space of stable log pairs of arbitrary dimension generalizing directly the space M_{g,n} of pointed stable curves. Each stable pair has semi log canonical…

We derive constraints on Lagrangian embeddings in completions of certain stable symplectic fillings with semisimple symplectic cohomologies. Manifolds with these properties can be constructed by generalizing the boundary connected sum…

Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and transferred to abelian surfaces and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a…