The Hurwitz Form of a Projective Variety

TL;DR

This paper explores the Hurwitz form of projective varieties, focusing on its computational properties, relation to dual and Chow forms, and the significance of reduced degenerations on the Hurwitz polytope.

Contribution

It provides new insights into the computational aspects of the Hurwitz form and its connections to other geometric invariants.

Findings

Analysis of the Hurwitz form's properties

Relation between Hurwitz form, dual variety, and Chow form

Identification of reduced degenerations as special cases

Abstract

The Hurwitz form of a variety is the discriminant that characterizes linear spaces of complementary dimension which intersect the variety in fewer than degree many points. We study computational aspects of the Hurwitz form, relate this to the dual variety and Chow form, and show why reduced degenerations are special on the Hurwitz polytope.