# Sparse Versions of the Cayley-Bacharach Theorem

## TL;DR

This paper introduces combinatorial generalizations of the Cayley-Bacharach theorem, expanding its applicability and understanding through new combinatorial perspectives and induced maps.

## Contribution

It provides novel combinatorial generalizations of the Cayley-Bacharach theorem and introduces related induced maps, broadening the theorem's theoretical framework.

## Key findings

- New combinatorial generalizations of the Cayley-Bacharach theorem
- Development of induced maps related to these generalizations
- Enhanced understanding of the theorem's combinatorial structure

## Abstract

We give combinatorial generalizations of the Cayley-Bacharach theorem and induced map.