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We define the dimension 2g − 1 Faber-Hurwitz Chow/homology classes on the moduli space of curves, parametrizing curves expressible as branched covers of P 1 with given ramification...
We prove an analogue of Farb-Masur’s theorem that the lengthspectra metric on moduli space is “almost isometric” to a simple model V(S) which is induced by the cone metric over the complex of curves. ...
By a mathematical instanton of charge n, we understand a rank-2 algebraic vector bundle E on the 3-dimensional projective space P3 with Chern classes (1) c1(E) = 0, c2(E) = n, satisfying the vanishi...
We present the scalar moduli stabilization from the perspective of the real intrinsic geometry.
We use the framework of Quot schemes to give a novel description of the moduli spaces of stable n-pairs, also interpreted as gauged vortices on a closed Riemann surface  with target Matr×n(C), where ...
The moduli spaces of trigonal curves of odd genus g ≥ 5 are proven to be rational.
We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generaliza-tion of...
We study the inertia stack of [M_{0,n}/S_n], the quotient stack of the moduli stack of smooth genus 0 curves with n marked points via the action of the symmetric group S_n. Then we see how from this ...
This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two...
This paper studies formality of the differential graded algebra $RHom(E,E)$, where $E$ is a semistable sheaf on a K3 surface. The main tool is Kaledin's theorem on formality in families. For a large ...
We show that the Brauer group of any moduli space of stable pairs with fixed determinant over a curve is zero.
Let $M$ be the moduli space of rank $2$ stable bundles with fixed determinant of degree $1$ on a smooth projective curve $C$ of genus $g\ge 2$. When $C$ is generic, we show that any elliptic curve on...
Fix a prime number p. The aim of this paper is to define a complete moduli stack of degree-p covers Y → X, with Y a stable curve which is a G-torsor over X, for a suitable group scheme G/X. The curve ...
We give an Eynard-Orantin type topological recursion formula for the canonical Euclidean volume of the combinatorial moduli space of pointed smooth algebraic curves. The recursion comes from the edg...
We study exact and asymptotic enumerative aspects of the Hilbert series of the cohomology ring of the moduli space of stable pointed curves of genus zero. This manifold is related to the WDVV (Witten...

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