Minimal generators of the defining ideal of the Rees Algebra associated to monoid parametrizations

TL;DR

This paper provides a minimal generating set for the defining ideal of the Rees Algebra related to monoid hypersurface parametrizations, extending known results for plane curves to rational surfaces.

Contribution

It introduces a new method to determine minimal generators of the Rees Algebra for monoid hypersurfaces, including rational surfaces with specific resolutions.

Findings

Minimal generators for Rees Algebra of monoid hypersurfaces identified.

Extended known results from plane curves to rational surfaces.

Applicable to surfaces with Hilbert-Burch resolution and specific syzygy degrees.

Abstract

We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we recover a known description for rational parametrizations having a syzygy of minimal degree (\mu=1). We also show that our approach can be applied to parametrizations of rational surfaces having a Hilbert-Burch resolution with \mu_1=\mu_2=1.