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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The Mori cones of moduli spaces of pointed curves of small genus
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by Gavril Farkas and Angela Gibney PDF
Trans. Amer. Math. Soc. 355 (2003), 1183-1199 Request permission

Abstract:

We compute the Mori cones of the moduli spaces $\overline M_{g,n}$ 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 $\overline M_g$ 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 $\overline M_{0,6}$, thus verifying Fulton’s conjecture for this space. Using this description we obtain a classification of all the fibrations of $\overline M_{0,6}$.
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Additional Information
  • Gavril Farkas
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
  • Email: gfarkas@umich.edu
  • Angela Gibney
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
  • MR Author ID: 689485
  • Email: agibney@umich.edu
  • Received by editor(s): February 25, 2002
  • Published electronically: November 7, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 1183-1199
  • MSC (2000): Primary 14H10
  • DOI: https://doi.org/10.1090/S0002-9947-02-03165-3
  • MathSciNet review: 1938752