Proves Eff^k(ar M_{g,n}) has infinitely many extremal rays for k≥2, g≥3, n≥2k-2; is non-polyhedral for k≥2, g≥1, n≥k+5; and every rational tails boundary stratum is extremal, via refined use of nef kappa divisors.
On the cone of effective 2-cycles on M0,7
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Extremal Effective Cycles and Nef Line Bundles on \(\overline{\rm{M}}_{g,n}\)
Proves Eff^k(ar M_{g,n}) has infinitely many extremal rays for k≥2, g≥3, n≥2k-2; is non-polyhedral for k≥2, g≥1, n≥k+5; and every rational tails boundary stratum is extremal, via refined use of nef kappa divisors.