9 problems

Let $I(a_{1}+m,dots,a_{n}+m)$ denote the toric ideal associated to the sequence $(a_{1}+m,dots,a_{n}+m)$, where $m\geq 0$ is an integer. HerzogSrinivasan conjecture. The Betti numb…

Let $C$ be a Gorenstein monomial curve of Stöhr–Torres type. Stöhr–Torres non-smoothability conjecture. The curve $C$ is not smoothable. The conjecture is motivated by the example…

Let $m_{0}<\cdots<m_{e}$ be an arithmetic sequence of positive integers, and let the associated affine monomial curve have homogeneous coordinate ring. Write $m_{0}\equiv a\pmod e$…

Let $u>1$, and let ${\mathcal C}_{u,d}$ be the monomial plane curve parametrized by the monomials $T_0^d$, $T_0^{d-u}T_1^u$, and $T_1^d$. Let $\Phi_0$ be the presentation map defin…

Let $\underline{a}=(a_0,\ldots,a_n)$ be a sequence of positive integers, let $j$ be a positive integer, and write $\underline{a}+(\underline{j})=(j+a_0,\ldots,j+a_n)$. Let…

Let ${\bf m}=\{m_1,\ldots,m_n\}$ be a sequence of positive integers. A class $C({\bf m})$ consists of monomial curves defined by increasing sequences…

Let $B$ be the affine semigroup under consideration, let $B_A$ denote its simplicial subsemigroup, and let $\sim$ be the equivalence relation on $B$. For $x,y\in B$, define … For…

Let $({\bf m})=m_0,\ldots,m_n$ be an arithmetic sequence of positive integers, and let $C({\bf m})\subset\mathbb A_k^{n+1}$ be the associated affine monomial curve, with homogeneou…

Let $A$ be a regular local ring and let $P$ be a dimension-one prime ideal of $A$. A blowup of $P$ is the scheme obtained from the Rees algebra of $P$ by taking its projective spec…