Virtual residue and generalized Cayley- Bacharach Theorem

TL;DR

This paper extends the Cayley-Bacharach Theorem to higher-dimensional cases using the concept of virtual residue, a generalization of Grothendieck residue, broadening its applicability in algebraic geometry.

Contribution

The paper introduces a generalized version of Cayley-Bacharach Theorem applicable to positive-dimensional cases through virtual residue.

Findings

Generalization of Cayley-Bacharach Theorem to positive dimensions

Application of virtual residue in algebraic geometry

Broader understanding of residue theory in geometric contexts

Abstract

Using virtual residue, which is a generalization of Grothendieck residue, we generalized Cayley- Bacharach Theorem to the cases with positive dimensions.