Regularity of primes associated with polynomial parametrisations

TL;DR

This paper establishes a doubly exponential bound on the Castelnuovo-Mumford regularity for prime ideals defining polynomially parametrized varieties, advancing understanding of algebraic complexity in geometric contexts.

Contribution

It provides the first doubly exponential bound on regularity for prime ideals associated with polynomial parametrizations, a significant theoretical advancement.

Findings

Doubly exponential bound on regularity established

Improves understanding of algebraic complexity in polynomial parametrizations

Advances theoretical bounds in algebraic geometry

Abstract

We prove a doubly exponential bound for the Castelnuovo-Mumford regularity of prime ideals defining varieties with polynomial parametrisation.