5 problems

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…

Herzog–Stamate conjecture.

Let $K$ be a field, let ${\mathbf a}=(a_1<\cdots<a_n)$ be a sequence of positive integers, and let $I({\mathbf a}+j)$ be the defining ideal of the affine monomial curve parametrize…

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…