P-Forms from Syzygies

Abstract

These notes aim to develop a tool for constructing polynomial differential $p$-forms vanishing on prescribed loci through syzygies of homogeneous ideals. Examples are provided through implementing this method in Macaulay2, particularly examples of instanton bundles of charges $4$ and $5$ on ${\mathbb{P}}^3$ that arise in this construction.

Comments welcome! To appear in RIMUT,