4 problems

Let $(R,\mathfrak{m},\Bbbk)$ be a regular local ring, let $I$ be a perfect ideal of grade $3$, and let $\operatorname{Tor}^R(R/I,\Bbbk)$ be its Tor algebra. The Tor algebra is said…

For a codimension-three licci ideal $I$, let $r$ denote the parameter of its Tor-algebra class $G(r)$, and let the number of generators of $I$ be fixed. The licci Tor-algebra class…

Let $Q$ be a standard graded polynomial ring over a field, let $R$ be a graded quotient of $Q$, and suppose that its Tor algebra has the form … where $\mathsf{P}$ is a graded algeb…

Let $S=K[x_1,dots,x_n]$ be a standard graded polynomial ring, and let $I,J\subset S$ be homogeneous ideals. Write $I^{\mathrm{lex}}$ for the lex ideal with the same Hilbert functio…