Moduli spaces of weighted pointed stable curves

Abstract

We compute the Mori cones of the moduli spaces M g,n of n pointed stable curves of genus g, when g and n are relatively small. For instance we show that for g < 14 every curve in M g is equivalent to an effective combination of the components of the locus of curves with 3g − 4 nodes. We completely describe the cone of nef divisors for the space M 0,6 , thus verifying Fulton's conjecture for this space. Using this description we obtain a classification of all the fibrations of M 0,6 .

Sharp slope bounds for sweeping families of trigonal curves

“…P is a connected nodal curve of genus zero, P is a balanced orbi-nodal curve in the sense of [1] with coarse space P → P , C is a connected orbi-nodal curve of genus g, φ : C → P is a twisted admissible cover of degree 3 in the sense of [1], (P, br φ) is a w-stable pointed curve in the sense of [13] with w = ( 2 ). For the convenience of the reader, we briefly recall the meanings of some of the terms.…”

Log canonical models for the moduli space of curves: The first divisorial contraction

“…[HKT06]). These can be understood explicitly in special cases, e.g., (M 0,n , δ) is a log canonical model [Has03,7.1]. Throughout, we work over an algebraically closed field k of characteristic zero.…”

Moduli Spaces of Rational Weighted Stable Curves and Tropical Geometry

“…These spaces were introduced by Hassett [13] in the context of the log minimal model program. In particular, he proves that there exists a smooth projective scheme representing the moduli problem of w-weighted stable curves.…”