Towards the ample cone of \overline{}_{,}

By A. Gibney, S. Keel, Ian A Morrison. 2000

97 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7256355f61f04f698403c4ab6eee4499884310e5

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Citations in the corpus

$\overline{M}_{0,n}$ is not a Mori Dream Space (2013, background): “ibing the ample divisors, i.e., the nef cone. A long standing conjecture of Fulton and Faber provides a conjectural description, which was reduced to the case of genus 0 by Gibney, Keel, and Morrison [GKM02]. This prompted Hu and Keel [HK00] to raise the question if M 0;n is a Mori Dream Space. In p”
Log canonical models for the moduli space of curves: The first divisorial contraction (2006, methodology): “ies in the interior of the facet R⊥ of the nef cone of M g. The following conjectural description of the ample cone of Mg,n would end the discussion in one stroke: Conjecture 4.3 (Fulton’s conjecture [GKM02]). Every one-dimensional facet of the closed cone of eﬀective curves NE1(Mg,n) is generated b”
The Kodaira dimension of moduli spaces of curves with marked points (2001, methodology): “(Gibney, Keel, and Morrison have recently made notable progress on these problems [ GKM ].) Rather, I will compute the classes of a number of divisors on Mg,n, and apply these results to determine the Kodaira dimension of many of the varieties Mg,n.”
Moduli spaces of weighted pointed stable curves (2002, methodology): “ﬁcation. The Losev-Manin moduli space is the ﬁrst step of the factorization described in §6.1. 31 7 Interpretations as log minimal models of moduli spaces Recently, Keel and his collaborators [KeMc1],[GKM],[G],[Ru] have undertaken a study of the birational geometry of the moduli space of curves, wit”
The mori cones of moduli spaces of pointed curves of small genus (2001, methodology): “n/S g. We note that Theorem 3 should be compared to Gibney’s result that for g≥ 2 any ﬁbration of M g,n factors through a projection to some M g,i (i<n) dropping some of the marked points (cf. [G],[GKM], Corollary 0.10). Paradoxically, because of the combinatorial complexity of Pic(M0,n), the ﬁbr”
Alternate Compactifications of Moduli Spaces of Curves (2010, background): “w. Nevertheless, two recent results comprise substantial evidence for the F-conjecture: First, Gibney, Keel, and Morrison have shown that if the Fconjecture holds for M0;g+n=Sg, then it holds for Mg;n[GKM02]. In particular, it is sucient to prove the conjecture for M0;nfor all n, where it appears so”