4 problems

Let $R/I$ be a Cohen–Macaulay algebra with minimal free resolution … For each $i$, let $m_i=\min\{d_{i,j}\mid j\in J_i\}$ be the minimum degree shift and let…

Let $R$ be the quotient ring defined by $n+1$ general quadrics in $n$ variables, with $n\geq 5$ odd, and write $\ell$ for the parameter governing the strands in its minimal graded…

Let $\mathcal{I}=k[2V_1\oplus V_3]^{SL_2}$ be an algebra of $SL_2$-invariants, and let $\beta_{i,j}$ denote its graded Betti numbers, with homological length $l$ and maximal intern…

Let $R=k[x_1,x_2,\ldots,x_n]$ be a standard graded polynomial ring over a field, and let $I\subset R$ be a homogeneous ideal of codimension $h$. Let $e(R/I)$ be the multiplicity of…