The Minimal Resolution Conjecture on a general quartic surface in $\mathbb P^3$
Abstract
Musta\c{t}\u{a} has given a conjecture for the graded Betti numbers in the minimal free resolution of the ideal of a general set of points on an irreducible projective algebraic variety. For surfaces in this conjecture has been proven for points on quadric surfaces and on general cubic surfaces. In the latter case, Gorenstein liaison was the main tool. Here we prove the conjecture for general quartic surfaces. Gorenstein liaison continues to be a central tool, but to prove the existence of our links we make use of certain dimension computations. We also discuss the higher degree case, but now the dimension count does not force the existence of our links.
Cite
@article{arxiv.1707.05646,
title = {The Minimal Resolution Conjecture on a general quartic surface in $\mathbb P^3$},
author = {Mats Boij and Juan C. Migliore and Rosa María Miró-Roig and Uwe Nagel},
journal= {arXiv preprint arXiv:1707.05646},
year = {2018}
}
Comments
16 pages, to appear in J. Pure Appl. Algebra. Proof of the main theorem has been substantially revised