Title: Equations of $\,\overline{M}_{0,n}$,
Abstract: Following work of Keel and Tevelev, we give explicit polynomials in the Cox
ring of $\mathbb{P}^1\times\cdots\times\mathbb{P}^{n-3}$ that, conjecturally,
determine $\overline{M}_{0,n}$ as a subscheme. Using Macaulay2, we prove that
these equations generate the ideal for $n=5, 6, 7, 8$. For $n \leq 6$ we give a
cohomological proof that these polynomials realize $\overline{M}_{0,n}$ as a
projective variety, embedded in $\mathbb{P}^{(n-2)!-1}$ by the complete log
canonical linear system.