4 problems

Ideal Generation Conjecture. The conjecture holds if

The surface Minimal Resolution Conjecture. The Betti table has the displayed shape

Let $S\subset\mathbb{P}^3$ be a very general surface of degree $d\geq4$, and let $\mathscr{L}=\mathscr{L}_e^S(m_1,\ldots,m_r)$ be a general fat point series. Classification conject…

Let $S\subset\mathbb{P}^3$ be a very general surface of degree at least $4$, and let $p_1,\ldots,p_r$ be general points on $S$. For multiplicities $m_1,\ldots,m_r$, write…