$s{l}_2$ conformal block divisors and the nef cone of ${\bar{M}}_{0,n}$

Abstract

We show that $s{l}_2$ conformal block divisors do not cover the nef cone of ${\bar{M}}_{0,6}$, or the $S_9$-invariant nef cone of ${\bar{M}}_{0,9}$. A key point is to relate the nonvanishing of intersection numbers between these divisors and F-curves to the nonemptiness of some explicitly defined polytopes. Several experimental results and some open problems are also included.

arXiv comment16 pages

References in corpus (3)

• Contractible Extremal Rays on \overline{M}_{0,n}
• Nef divisors on ${\bar{M}}_{0,n}$ from GIT
• The cone of type A, level one conformal blocks divisors

Cited by in corpus (7)

• The Chern classes of the Verlinde bundles
• Semiampleness criteria for divisors on ${\overline{M}}_{0,n}$
• Nonvanishing of conformal blocks divisors on ${\bar{M}}_{0,n}$
• On $S_n$-invariant conformal blocks vector bundles of rank one on ${\overline{M}}_{0,n}$
• Scaling of conformal blocks and generalized theta functions over ${\bar{M}}_{g,n}$
• New nef divisors on ${\bar{M}}_{0,n}$
• Basepoint free cycles on ${\overline{M}}_{0,n}$ from Gromov-Witten theory