Blowup algebras of rational normal scrolls

TL;DR

This paper explicitly describes the equations of the blowup of projective space along a rational normal scroll and proves that associated Rees and special fiber rings are Koszul algebras, advancing algebraic geometry understanding.

Contribution

It provides explicit equations for the blowup of projective space along rational normal scrolls and establishes Koszulness of related Rees and fiber rings, a novel result in the field.

Findings

Explicit equations for the blowup along rational normal scrolls

Proof that Rees and fiber rings are Koszul algebras

Enhanced understanding of algebraic structures of blowups

Abstract

We determine the equations of the blowup of $\mathbb{P}^n$ along a $d$-fold rational normal scroll $S$, and we prove that the Rees ring and special fiber ring of $S \subseteq \mathbb{P}^n$ are Koszul algebras.