Basepoint free cycles on ${\overline{M}}_{0,n}$ from Gromov-Witten theory

Abstract

Basepoint free cycles on the moduli space ${\overline{M}}_{0,n}$ of stable n-pointed rational curves, defined using Gromov-Witten invariants of smooth projective homogeneous spaces X are studied. Intersection formulas to find classes are given, with explicit examples for X a projective space, and X a smooth projective quadric hypersurface. When X is projective space, divisors are shown equivalent to conformal blocks divisors for type A at level one, giving maps from ${\overline{M}}_{0,n}$ to birational models constructed as GIT quotients, parametrizing configurations of weighted points supported on (generalized) Veronese curves.

24 pages

References in corpus (3)

• $s{l}_2$ conformal block divisors and the nef cone of ${\bar{M}}_{0,n}$
• A polygonal presentation of $Pic({\overline{\mathfrak{M}}}_{0,n})$
• Semiampleness criteria for divisors on ${\overline{M}}_{0,n}$