7 problems

Multivariable additivity conjecture. The conclusion of Theorem $$ still holds for three or more variables.

Let $(X,L)$ be as in case $2)$, and let $P(z)$ be its Hilbert polynomial. Let $R(x,y)$ be the polynomial from Proposition, and consider the factor of $P(z)$ corresponding to…

Let $(X,L)$ be as in $(\diamond)$, with $X=\mathbb P(\mathcal E)$ an $n$-dimensional Fano bundle over $Y$, and with $\operatorname{rk}(\mathcal E)\geq\dim Y$ (equivalently,…

Let $K$ be the ground field, let $\mathbb W=m_1P_1+\cdots+m_sP_s$ be a fat point scheme in $\mathbb P^n$, and let … Write $R_{\mathbb W}$ for the homogeneous coordinate ring of…

Regularity conjecture for amenable d-sequences. If ${\mathbf x}$ is an amenable d-sequence relative to $M$,

Let $(B,H,C)$ be a homology triplet, and let $\mathcal{E}^{\bullet}$ be a complex of coherent sheaves corresponding to it as in the realization conjecture. Hilbert-polynomial uniqu…

Let $X=\mathbb{P}^1\times\mathbb{P}^1$. A vector bundle on $X$ has a bigraded Hilbert polynomial, and write this polynomial as $\chi(s_1,s_2)$. Eisenbud–Schreyer's Hilbert polynomi…