Multigraded Cayley-Chow forms

TL;DR

This paper develops a new theory of multigraded Cayley-Chow forms for subvarieties in product of projective spaces, revealing dimension inequalities and multiplicity phenomena, with applications to computer vision.

Contribution

It introduces a novel framework for multigraded Cayley-Chow forms, highlighting new geometric phenomena and connecting to multifocal tensors in computer vision.

Findings

Dimension inequalities are necessary for the construction.

Multigraded Cayley-Chow forms can have higher multiplicities in positive characteristic.

Framework enhances understanding of multifocal tensors in computer vision.

Abstract

We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections; and second, in positive characteristic the multigraded Cayley-Chow forms can have higher multiplicities. The theory also provides a natural framework for understanding multifocal tensors in computer vision.