# The mori cones of moduli spaces of pointed curves of small genus

@article{Farkas2001TheMC, title={The mori cones of moduli spaces of pointed curves of small genus}, author={G. Farkas and A. Gibney}, journal={Transactions of the American Mathematical Society}, year={2001}, volume={355}, pages={1183-1199} }

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 Mg 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 .

#### 63 Citations

On Log Canonical Models of the Moduli Space of Stable Pointed Curves

- Mathematics
- 2007

We study the log canonical models of the moduli space MBar_{0,n} of pointed stable genus zero curves with respect to the standard log canonical divisors K+aD, where D denotes the boundary. In… Expand

MORI'S PROGRAM FOR THE MODULI SPACE OF POINTED STABLE RATIONAL CURVES

- Mathematics
- 2010

We prove that, assuming the F-conjecture, the log canonical model of the pair (M0;n; P ai i) is the Hassett's moduli space M0;A without any modification of weight coefficients. For the boundary… Expand

Positive divisors on quotients of M¯0,n and the Mori cone of M¯g,n

- Mathematics
- 2009

We prove that if m=n-3 then every Sm-invariant F-nef divisor on the moduli space of stable n-pointed curves of genus zero is linearly equivalent to an effective combination of boundary divisors. As… Expand

Applied Mori theory of the moduli space of stable pointed rational curves

- Mathematics
- 2011

We investigate questions motivated by Mori’s program for the moduli space of stable pointed rational curves, M0,n. In particular, we study the nef cone of M0,n (Chapter 2), the Cox ring of M0,n… Expand

On the birational geometry of the moduli of hyperelliptic curves

- Mathematics
- 2021

We study the birational geometry of the moduli spaces of hyperelliptic curves with marked points. We complete the Kodaira classification proving that these spaces are of Calabi-Yau type when the… Expand

Cyclic covering morphisms on M 0 , n

- 2011

We study cyclic covering morphisms from M0,n to moduli spaces of unpointed stable curves of positive genus or compactified moduli spaces of principally polarized abelian varieties. Our main… Expand

Log canonical models for the moduli space of pointed stable rational curves

- Mathematics
- 2011

We run Mori's program for the moduli space of pointed stable rational curves with divisor $K +\sum a_{i}\psi_{i}$. We prove that, without assuming the F-conjecture, the birational model for the pair… Expand

Log canonical models for the moduli space of stable pointed rational curves

- Mathematics
- 2013

We run Mori’s program for the moduli space of stable pointed rational curves with divisor K + ∑ aiψi. We prove that the birational model for the pair is either the Hassett space of weighted pointed… Expand

Numerical criteria for divisors on M g to be ample

- 2009

The moduli space Mg,n of n-pointed stable curves of genus g is stratified by the topological type of the curves being parameterized: the closure of the locus of curves with k nodes has codimension k.… Expand

Hodge classes on the moduli space of W(E_6)-covers and the geometry of A_6

- Mathematics
- 2021

In previous work we showed that the Hurwitz space of W (E6)-covers of the projective line branched over 24 points dominates via the Prym-Tyurin map the moduli space A6 of principally polarized… Expand

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