Related papers: Calculating intersection numbers on moduli spaces …

Goulden, Jackson and Vakil observed a polynomial structure underlying one-part double Hurwitz numbers, which enumerate branched covers of $\mathbb{CP}^1$ with prescribed ramification profile over $\infty$, a unique preimage over 0, and…

The main subject is the difference between the coarse moduli space and the stack of hyperelliptic curves. In particular, we compute their Picard groups, giving explicit description of the generators. We also study how many families of…

We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. The calculations of…

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…

This paper studies intersection theory on the compactified moduli space M(n,d) of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface of genus g > 1 where n and d may have common factors. Because of the presence…

We investigate the (small) quantum cohomology ring of the moduli spaces of stable n-pointed curves of genus 0. In particular, we determine an explicit presentation in the case n=5 and we outline a computational approach to the case n=6.

In a 1992 paper, Witten gave a formula for the intersection pairings of the moduli space of flat $G$-bundles over an oriented surface, possibly with markings. In this paper, we give a general proof of Witten's formula, for arbitrary…

For the pure $\psi$-class intersection numbers $D(\textbf{e})=\langle \tau_{e_1} \cdots \tau_{e_n} \rangle_g$ on the moduli space $\overline{\mathcal{M}}_{g,n}$ of stable curves, we determine for which choices of $\textbf{e}=(e_1, \ldots,…

The slope of the moduli space of genus g curves is bounded from below by 60/(g+4) via a descendent calculation.

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…

We compute the intersection Betti numbers of the GIT model of the moduli space of Brill-Noether-Petri general curves of genus 4. This space was shown to be the final non-trivial log canonical model for the moduli space of stable genus four…

We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for…

Kontsevich's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on $N\times N$ matrices and N-point…

This paper focuses on the interplay between the intersection theory and the Teichmueller dynamics on the moduli space of curves. As applications, we study the cycle class of strata of the Hodge bundle, present an algebraic method to…

We prove an estimate on intersection pairing of homology classes in hyperbolic 4-manifolds in terms of Thurston norms of these classes.

We study the moduli stacks of real vector bundles of fixed rank and degree on a type I real algebraic curve and determine its mod 2 cohomology algebra in terms of characteristic classes.

This is the authors doctoral thesis written at the Humboldt-University Berlin. It contains material from the three separate papers: "On the Kodaira dimension of the moduli space of nodal curves", "On quotients of…

We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by…

We extend the methods developed in our earlier work to algorithmically compute the intersection cohomology Betti numbers of reductive varieties. These form a class of highly symmetric varieties that includes equivariant compactifications of…

We establish new bounds on the number of tangencies and orthogonal intersections determined by an arrangement of curves. First, given a set of $n$ algebraic plane curves, we show that there are $O(n^{3/2})$ points where two or more curves…