A non-boundary nef divisor on $\bar{M}_{0,12}$

TL;DR

This paper constructs a specific nef divisor on the moduli space of 12-pointed rational curves that cannot be expressed as a sum of boundary divisors, challenging previous assumptions about divisor decompositions.

Contribution

It introduces a non-boundary nef divisor on M_{0,12} that is not numerically equivalent to an effective sum of boundary divisors, providing a counterexample in the study of divisor classes.

Findings

Existence of a nef divisor not equivalent to boundary sums on M_{0,12}

Counterexample to boundary divisor decomposition conjecture

Advances understanding of divisor class structure on moduli spaces

Abstract

We describe a nef divisor $D_P$ on $\bar{M}_{0,12}$ that is not numerically equivalent to an effective sum of boundary divisors.