Multigraded Hurwitz forms

TL;DR

This paper extends the concept of Hurwitz forms to multigraded settings in products of projective spaces, providing explicit degree formulas for complete intersections and demonstrating applications in elimination theory with diverse fields.

Contribution

It introduces multigraded Hurwitz forms, extending classical notions, and derives explicit degree formulas for complete intersections, enhancing tools for elimination theory.

Findings

Derived explicit degree formulas for multigraded Hurwitz forms

Extended Hurwitz forms to varieties in product of projective spaces

Applied results to areas like Nash equilibria and Feynman integrals

Abstract

The Hurwitz form of a projective variety characterizes linear spaces of complementary dimension which meet the variety non-transversally. We extend this notion to varieties in a product of projective spaces. This parallels the multigraded Chow forms due to Osserman and Trager. We study the degrees of multigraded Hurwitz forms. An explicit degree formula is given for complete intersections. This offers a new tool for elimination theory that has many applications, ranging from Nash equilibria to Feynman integrals.