Related papers: An Effective Divisor in $\overline{M_{g}}$ Defined…

We prove two statements on the slopes of effective divisors on the moduli space of stable curves of genus g: first that the Harris-Morrison Slope Conjecture fails for g=10 and second, that in order to compute the slope of the moduli space…

We compute many new classes of effective divisors in $\overline{\mathcal{M}}_{g,n}$ coming from the strata of abelian differentials and efficiently reproduce many known results obtained by alternate methods. Our method utilises maps between…

We describe a systematic way of constructing effective divisors on the moduli space of stable curves of genus g having exceptionally small slope. We prove that any divisor on \bar{M}_g consisting of curves failing a certain Green-Lazarsfeld…

We carry out a detailed intersection theoretic analysis of the Deligne-Mumford compactification of the divisor on M_{10} consisting of curves sitting on K3 surfaces. This divisor is not of classical Brill-Noether type, and is known to give…

We compute the class of the effective divisors on $\overline{\mathcal{M}}_{g,n}$, which are set theoretically equal to the locus of moduli points $[C,p_1,\dots ,p_n]$ where $C$ lies on a quadric under the map given by the linear series…

Let M_g be the moduli space of smooth curves of genus g >= 3, and \bar{M}_g the Deligne-Mumford compactification in terms of stable curves. Let \bar{M}_g^{[1]} be an open set of \bar{M}_g consisting of stable curves of genus g with one node…

This paper is a sequel to \cite{C}, in which the author studies secant planes to linear series on a curve that is general in moduli. In that paper, the author proves that a general curve has no linear series with exceptional secant planes,…

Given a moduli problem with a nice coarse moduli space, which is the most intrinsic and natural divisor on this moduli space? We describe a general method of constructing effective divisors on a large class of moduli spaces using the…

We construct vector-valued modular forms on moduli spaces of curves and abelian varieties using effective divisors in projectivized Hodge bundles over moduli of curves. Cycle relations tell us the weight of these modular forms. In…

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…

Let C be a general connected, smooth, projective curve of positive genus g. For each nonnegative integer i we give formulas for the number of pairs (P,Q) em C x C off the diagonal such that (g+i-1)Q-(i+1)P is linearly equivalent to an…

After a general discussion of group actions, orbifolds, and "weak orbifolds" this note will provide elementary introductions to two basic moduli spaces over the real or complex numbers: First the moduli space of effective divisors with…

Let X_n := \bar M_{0,n}, the moduli space of n-pointed stable genus zero curves, and let X_{n,m} be the quotient of X_n by the action of the symmetric group S_{n-m} on the last n-m marked points. The cones of effective divisors of X_{n,m},…

Let $X$ be a smooth projective complex curve of genus $g \geq 2$ and let $\M_X(2,\Lambda)$ be the moduli space of semi-stable rank-$2$ vector bundles over $X$ with fixed determinant $\Lambda$. We show that the wobbly locus, i.e., the locus…

We compute the class of the locus in M_g of curves having a pencil with two unspecified triple ramification points. This is the first example of a geometric divisor on M_g which is not the pull-back of a divisor on the moduli space of…

In this paper we consider an effective divisor on the complex projective line and associate with it the module D consisting of all the derivations $\theta$ such that $\theta(I_i)\subset I_i^{m_i}$ for every $i$, where $I_i$ is the ideal of…

For genus $g=2i\geq4$ and the length $g-1$ partition $\mu = (4,2,\ldots,2,-2,\ldots,-2)$ of 0, we compute the first coefficients of the class of $\overline{D}(\mu)$ in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{R}}_g)$, where $D(\mu)$ is…

We introduce and compute the class of a number of effective divisors on the moduli space of stable maps $\bar M_{0,0}(P^{r},d)$, which, for small d, provide a good understanding of the extremal rays and the stable base locus decomposition…

We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class group we exhibit an explicit basis consisting of boundary…

We describe the GIT compactification of the moduli of (2,2)-type effective divisors of $\mathbb{P}^1\times\mathbb{P}^2$ (i.e., surfaces of the linear system $\vert \pi_1^*\mathcal{O}_{\mathbb{P}^1}(2)\otimes…