Symbolic Blowup algebras of monomial curves in ${\mathbb{A}}^3$ defined by arithmetic sequence

Abstract

In this paper, we consider monomial curves in ${\mathbb{A}}_k^3$ parameterized by $t\to (t^{2q+1},t^{2q+1+m},t^{2q+1+2m})$ where $gcd(2q+1,m)=1$. The symbolic blowup algebras of these monomial curves is Gorenstein (\cite{goto-nis-shim}, \cite{goto-nis-shim-2}). We give a simple proof for the the Gorenstein property for the symbolic blowup algebras of these curves.

References in corpus (1)

• Symbolic Blowup algebras and invariants of certain monomial curves in an affine space