Groebner techniques for low degree Hilbert stability

Abstract

We give a method for verifying, by a symbolic calculation, the stability or semistability with respect to a linearization of fixed, possibly small, degree $m$, of the Hilbert point of a scheme $X\in \mathbb{P}(V)$ having a suitably large automorphism group. We also implement our method and apply it to analyze the stability of bicanonical models of certain curves. Our examples are very special, but they arise naturally in the log minimal model program for ${\bar{\mathcal{M}}}_g$. In some examples, this connection provides a check of our computations; in others, the computations confirm predictions about conjectural stages of the program.

25 pages, 2 figures, accompanying file of code samples

References in corpus (5)

• Log minimal model program for the moduli space of stable curves: The first flip
• Log minimal model program for the moduli space of stable curves of genus three
• A geometric invariant theory construction of moduli spaces of stable maps
• Modular compactifications of M_{1,n}
• GIT Constructions of Moduli Spaces of Stable Curves and Maps