Nef divisors on \( \M_{0,n} \) from GIT

  • Valery Alexeev

    University of Georgia, Athens, United States
  • David Swinarski

    Fordham University, Bronx, USA
Nef divisors on $\M_{0,n}$ from GIT cover
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We introduce and study the GIT cone of M0,n\overline{M}_{0,n}, which is generated by the pullbacks of the natural ample line bundles on the GIT quotients (P1)n/ ⁣/SL(2)(\mathbb P^1)^n/\!/SL(2). We give an explicit formula for these line bundles and prove a number of basic results about the GIT cone. As one application, we prove unconditionally that the log canonical models of M0,n\overline{M}_{0,n} with a symmetric boundary divisor coincide with the moduli spaces of weighted curves or with the symmetric GIT quotient, extending the result of Matt Simpson.