Related papers: Pseudostable Hodge integrals
We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for all intersection numbers on the hyperelliptic locus with one $\lambda$-class, and powers…
In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and it is endowed with a scheme structure. We introduce a relative version of the Krichever map using a fibration of Sato…
In this paper, we consider an arithmetic Hodge index theorem for a family of semi-stable curves f: X \to B with f_{\bf C} being smooth, generalizing Faltings-Hriljac's arithmetic Hodge index theorem for an arithmetic surface.
In this paper, we deal with stable homology computations with twisted coefficients for mapping class groups of surfaces and of 3-manifolds, automorphism groups of free groups with boundaries and automorphism groups of certain right-angled…
In this paper for each $n\ge g\ge 0$ we consider the moduli stack $\widetilde{\mathcal U}^{ns}_{g,n}$ of curves $(C,p_1,\ldots,p_n,v_1,\ldots,v_n)$ of arithmetic genus $g$ with $n$ smooth marked points $p_i$ and nonzero tangent vectors…
We explore the cohomological structure for the (possibly singular) moduli of $\mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the…
We define and study the stack ${\mathcal U}^{ns,a}_{g,g}$ of (possibly singular) projective curves of arithmetic genus g with g smooth marked points forming an ample non-special divisor. We define an explicit closed embedding of a natural…
We show that moduli spaces of stable maps admits virtual orbifold structure. The symplectic version of virtual localization formula is obtained.
We develop a framework to construct moduli spaces of $\mathbb{Q}$-Gorenstein pairs. To do so, we fix certain invariants; these choices are encoded in the notion of $\mathbb{Q}$-stable pair. We show that these choices give a proper moduli…
We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack [point/GL(1)], and use it to construct some gauge-theoretic analogues of the Gromov-Witten invariants. We also indicate the…
The purpose of these notes is to give an introduction to Deligne-Mumford stacks and their moduli spaces, with emphasis on the moduli problem for curves. The paper has 4 sections. In section 1 we discuss the general problem of constructing a…
When a reductive group $G$ acts linearly on a complex projective scheme $X$ there is a stratification of $X$ into $G$-invariant locally closed subschemes, with an open stratum $X^{ss}$ formed by the semistable points in the sense of…
We present two approaches to the study of the cohomology of moduli spaces of curves. Together, they allow us to compute the rational cohomology of the moduli space \Mbar_4 of stable complex curves of genus 4, with its Hodge structure.
We present certain new properties about the intersection numbers on moduli spaces of curves $\bar{\sM}_{g,n}$, including a simple explicit formula of $n$-point functions and several new identities of intersection numbers. In particular we…
We prove the Gopakumar-Marino-Vafa formula for special cubic Hodge integrals. The GMV formula arises from Chern-Simons/string duality applied to the unknot in the three sphere. The GMV formula is a q-analog of the ELSV formula for linear…
We use techniques of Alper-Hall-Rydh to prove a local structure theorem for smooth morphisms between smooth stacks around points with linearly reductive stabilizers. This implies that the good moduli space of a smooth stack over a base has…
This largely expository paper first gives an introduction to Hilbert stability and its use in Gieseker's GIT construction of $\overline{M}_g$. Then I review recent work in this area--variants for unpointed curves that arise in Hassett's log…
In this survey article we give an overview of how noncongruence modular curves can be viewed as Hurwitz moduli spaces of covers of elliptic curves at most branched above the origin. We describe some natural questions that arise, and…
In the present thesis we study the geometry of the moduli spaces of Bradlow-Higgs triples on a smooth projective curve $C$. $(E,\varphi, s)$ is a Bradlow-Higgs triple if $(E,\varphi)$ is a Higgs bundle and $s$ is a non-zero global section…
This paper is the first in a series of four papers aiming to describe the (almost integral) Chow ring of $\bar{\mathcal{M}}_3$, the moduli stack of stable curves of genus $3$. In this paper, we introduce the moduli stack…