Related papers: The moduli space of stable n-pointed curves of gen…

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 this article we consider the moduli space of smooth $n$-pointed non-hyperelliptic curves of genus 3. In the pursuit of cohomological information about this space, we make $\mathbb{S}_n$-equivariant counts of its numbers of points defined…

We give a recursive algorithm for computing the character of the cohomology of the moduli space $\Mmb_{0,n}$ of stable $n$-pointed genus zero curves as a representation of the symmetric group $\Sg_n$ on $n$ letters. Using the algorithm we…

In this mostly expository paper we review several known results about the cohomology of moduli spaces of smooth and stable curves, focusing in particular on low degree cohomology. We also give a new proof of Harer's theorem describing the…

A weighted pointed curve consists of a nodal curve and a sequence of marked smooth points, each assigned a number between zero and one. A subset of the marked points may coincide if the sum of the corresponding weights is no greater than…

We consider the moduli space of rank two, odd degree, semi-stable Real vector bundles over a real curve, calculating the singular cohomology ring in odd and zero characteristic for most examples.

We prove that in a stable range, the rational cohomology of the moduli space of curves with level structures is the same as that of the ordinary moduli space of curves.

We compute the stable cohomology of moduli spaces of hyperelliptic curves of a fixed genus embedded on a fixed Hirzebruch surface. We also describe these moduli spaces of embedded hyperelliptic curves in terms of moduli spaces of pointed…

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 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 construct moduli spaces of representations of quivers over arbitrary schemes and show how moduli spaces of pointed curves of genus zero like the Grothendieck-Knudsen moduli spaces $\overline{M}_{0,n}$ and the Losev-Manin moduli spaces…

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…

We determine the cohomology of the Losev-Manin moduli space of pointed genus zero curves as a representation of the product of symmetric groups.

We compute the first, second, third, and fifth rational cohomology groups of the moduli space of stable n-pointed genus g curves, for all g and n, using (mostly) algebro-geometric techniques.

We calculate the quantum cohomology of the moduli space of stable $\PGL_2$-bundles over a smooth curve of genus $g\ge 2$.

We prove Koszulity of the homology of the of moduli spaces of stable n-pointed curves of genus zero $\overline{M}_{0,n}$ for $n=5$, using its presentation due to Keel and the Priddy criterion of Koszulity. For $n=6 $ we establish that…

The stable rationality of components of the moduli space of (unparametrized) rational curves in projective $n$-space with fixed normal bundle is proved, provided these components dominate the moduli space of immersed rational curves in the…

This note is about invariants of moduli spaces of curves. It includes their intersection theory and cohomology. Our main focus in on the distinguished piece containing the so called tautological classes. These are the most natural classes…

This is an expository paper. The geometry of phylogenetic trees is used to present in an accessible and pleasant fashion the results of Deligne, Mumford, and Knudsen about the moduli space of n distinct points on the projective line and its…

In a previous paper, arXiv:1301.4409, we showed that the moduli space of curves C with a G-symmetry (that is, with a faithful action of a finite group G), having a fixed generalized homological invariant, is irreducible if the genus g' of…