11 problems

Let $R=K[x_1,\ldots,x_n]$, and let $I$ be a homogeneous ideal containing a regular sequence of degrees $2\leq a_1\leq\ldots\leq a_n$. Suppose that there exists a lex-plus-powers id…

Evans's lex-plus-powers conjecture. For all $i,j$,

Top-socle Lex Plus Powers conjecture. Then

Lex Plus Powers conjecture for socles. Then

The Lex Plus Powers conjecture for Hilbert functions. Then

The Lex Plus Powers conjecture. If $\mathcal H$ is $\mathbb A$-lpp valid and $L_{\mathcal H,\mathbb A}$ is the $\mathbb A$-lex plus powers ideal attaining $\mathcal H$, then…

Let $R=K[x_1,\ldots,x_n]$, and let $I$ be a homogeneous ideal containing a regular sequence of degrees $2\leq a_1\leq\ldots\leq a_n$. Let $L$ be a lex-plus-powers ideal associated…

Let $R$ be a polynomial ring over an infinite field, and let $I\subseteq R$ be a homogeneous ideal containing a regular sequence in prescribed degrees. For a fixed Hilbert function…

Let $S=\Bbbk[x_{1},\ldots,x_{n}]$, let $(f_{1},\ldots,f_{r})$ be a regular sequence with $\deg f_i=e_i$, and set … Let $I$ be the homogeneous ideal containing this regular sequence…

Let $S=\Bbbk[x_{1},\ldots,x_{n}]$, let $F=(f_{1},\ldots,f_{r})$ be any homogeneous regular sequence with $\deg f_i=e_i$, and define … Let $I$ be any homogeneous ideal containing…

Let $S=\Bbbk[x_{1},\ldots,x_{n}]$, let $P=(x_{1}^{e_{1}},\ldots,x_{r}^{e_{r}})$, and let $F=(f_{1},\ldots,f_{r})$ be a homogeneous regular sequence with $\deg f_i=e_i$. Let $I$ be…