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This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…

For physicists: We show that the quiver gauge theory derived from a Calabi-Yau cone via an exceptional collection of line bundles on the base has the original cone as a component of its classical moduli space. For mathematicians: We use…

We give an algebraic construction of the moduli space of irregular singular connections of generic ramified type on a smooth projective curve. We prove that the moduli space is smooth and give its dimension. Under the assumption that the…

This paper studies the moduli space of stable surfaces of general type. The moduli space component containing the moduli point of a product of smooth curves of general type is proved to be the product of the moduli spaces of the curves,…

We show that on a generic curve, a bundle obtained by successive extensions is stable. We compute the dimension of the set of such extensions. We use degeneration methods specializing the curve to a chain of elliptic components

This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.

The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…

Moduli spaces of compact stable $n$-pointed curves carry a hierarchy of cohomology classes of top dimension which generalize the Weil-Petersson volume forms and constitute a version of Mumford classes. We give various new formulas for the…

We develop the theory of associating moduli spaces with nice geometric properties to arbitrary Artin stacks generalizing Mumford's geometric invariant theory and tame stacks.

We compute the effective cone for the moduli space of stable rational curves with at most six marked points.

We consider the stack of stable curves of genus g with a given dual graph and we give an explicit desingularization of its closure in the moduli stack of stable curves. We study in particular the one-dimensional substack of curves with at…

Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof of a theorem of Looijenga and…

Moduli of vector bundles on stacky curves behave similarly to moduli of vector bundles on curves, except there are additional numerical invariants giving many different notions of stability. We apply the existence criterion for good moduli…

We construct a moduli space of slope-semistable pure sheaves, building upon previous work of Le Potier and Jun Li on torsion-free sheaves over smooth surfaces. In particular, our construction provides a compactification of the Simpson…

This is the first of at least two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in R x (S^1 x S^2) as defined by a certain natural pair of almost complex structure and symplectic form. This…

The space of smooth rational cubic curves in projective space $\PP^r$ ($r\ge 3$) is a smooth quasi-projective variety, which gives us an open subset of the corresponding Hilbert scheme, the moduli space of stable maps, or the moduli space…

We prove that the moduli spaces of n-pointed m-stable curves introduced in our previous paper have projective coarse moduli. We use the resulting spaces to run an analogue of the Hassett-Keel log minimal model program for the moduli space…

We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We…

Given a curve over a finite field, we compute the number of stable bundles of not necessarily coprime rank and degree over it. We apply this result to compute the virtual Poincare polynomials of the moduli spaces of stable bundles over a…

In this article we will construct a universal moduli space of stable parabolic vector bundles over the moduli space of marked Deligne-Mumford stable curves $\overline{M}_{_{g, n}}$. The objects that appear over the boundary of…