6 problems

Let $X\subset \mathbb{P}^r$ be a projective variety, let $\Gamma\subset X$ be a set of $\gamma$ general points, and let $b_{i,j}(\Gamma)$ denote its graded Betti numbers. Let $u$ b…

Let $X$ be the ambient variety and let $\Gamma$ be a set of points with ideals $I_X$ and $I_\Gamma$. Write $b_{i,j}$ for the relevant graded Betti numbers in the minimal free resol…

Weakened Minimal Resolution Conjecture. The set $X$ has a generic Hilbert matrix as in the source definition, and, for every fixed $(i,j)>(0,0)$, one has $\beta_{1,(i,j)}>0$ if and…

Let $Q$ be a pointed affine semigroup with group of automorphisms $G$, let $\Bbbk$ be a field of characteristic $p>0$, and let $\Bbbk'$ be the field extension used in an intrinsic…

Let $I$ be a monomial ideal with a minimal resolution supported on a regular CW-complex having the intersection property, meaning that the intersection of any two cells is also a c…

Let $C\subset \mathbb{P}^r$ be a smooth curve of genus $g$ embedded by a linear series $\ell=(L,V)\in G^r_d(C)$, and let $\Gamma\subset C$ be a set of $\gamma$ general points with…