相关论文: On the effective cone of $\overline{\mathcal{M}}_{…

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…

For every $n\geq 3$, we exhibit infinitely many extremal effective divisors on the moduli space of genus one curves with $n$ marked points.

For $g\geq2$, $j=1,\dots,g$ and $n\geq g+j$ we exhibit infinitely many new rigid and extremal effective codimension $j$ cycles in $\overline{\mathcal{M}}_{g,n}$ from the strata of quadratic differentials and projections of these strata…

We review and develop some techniques used to investigate the effective cones of higher codimension classes. Our results show that a large collection of boundary strata of rational tails type are extremal in their effective cones on…

We show that certain divisors of Brill-Noether and Gieseker-Petri type span extremal rays of the effective cone in the moduli space of stable genus one curves with $n$ ordered marked points. In particular, they are different from the…

We develop a new method for establishing the extremality in the closed cone of effective curves on the moduli space of curves and determine the extremality of many boundary $1$-strata. As a consequence, by using a general criterion for…

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…

We study effective divisors on $\overline{M}_{0,n}$, focusing on hypertree divisors introduced by Castravet and Tevelev and the proper transforms of divisors on $\overline{M}_{1,n-2}$ introduced by Chen and Coskun. Results include a…

We exhibit infinitely many extremal effective codimension-$k$ cycles in $\overline{\mathcal{M}}_{g,n}$ in the cases $g\geq 3, n\geq g-1$ and $k=2$, $g\geq 2$, $k\leq n-g,g,$ and $g=1$, $k\leq n-2$. Hence in these cases the effective cone is…

We show that certain geometrically defined higher codimension cycles are extremal in the effective cone of the moduli space $\overline{\mathcal M}_{g,n}$ of stable genus $g$ curves with $n$ ordered marked points. In particular, we prove…

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},…

This paper is an expository survey of results about the effective divisors on moduli spaces, with a focus on what is known about the effective cones of moduli spaces of stable curves and of principally polarized abelian varieties. This…

We prove that the nonvarying strata of abelian and quadratic differentials in [CM1, CM2] have trivial tautological rings and are affine varieties. We also prove that strata of $k$-differentials of infinite area are affine varieties for all…

In this paper we study the ample cone of the moduli space $\mgn$ of stable $n$-pointed curves of genus $g$. Our motivating conjecture is that a divisor on $\mgn$ is ample iff it has positive intersection with all 1-dimensional strata (the…

We compute the class of the closure of the locus of canonical divisors in the projectivization of the Hodge bundle $\mathbb{P}\overline{\mathcal{H}}_g$ over $\overline{\mathcal{M}}_g$ which have a zero at a Weierstrass point. We also show…

We show that the pseudoeffective cone of divisors $\overline{\text{Eff}}^1(\overline{\mathcal{M}}_{g,n})$ for $g\geq 2$ and $n\geq 2$ is not polyhedral by showing that the class of the fibre of the morphism forgetting one point forms an…

The divisors on $\bar{\operatorname{M}}_g$ that arise as the pullbacks of ample divisors along any extension of the Torelli map to any toroidal compactification of $\operatorname{A}_g$ form a 2-dimensional extremal face of the nef cone of…

On a weighted projective surface $\mathbb{P}(a,b,c)$ with $\min(a,b,c)\leq 4$, we compute lower bounds for the {\em effective threshold} of an ample divisor, in other words, the highest multiplicity a section of the divisor can have at a…

This is the second of two papers on the birational geometry of $\bar{M}_{g,1}$. We construct rational maps from $\bar{M}_{5,1}$ and $\bar{M}_{6,1}$ to lower-dimensional moduli spaces. As a consequence, we identify geometric divisors that…

We compute a closed formula for the class of the closure of the locus of curves in $\overline{\mathcal{M}}_g$ that admit an abelian differential of signature $\kappa=(k_1,...,k_{g-2})$.