@article{62a8e8f014af4173be5c2c93ac2f351f,
title = "Sparse versions of the Cayley-Bacharach theorem",
abstract = "We give combinatorial generalizations of the Cayley-Bacharach theorem and induced map.",
keywords = "Cayley-Bacharach, resultants",
author = "Matusevich, {Laura Felicia} and Bruce Reznick",
note = "Funding Information: LFM was partially supported by NSF Grant DMS-1500832. BR was partially supported by Simons Collaboration Grant 280987. Funding Information: This project has benefited from visits by the authors to each other?s institutions. We also discussed this material during the joint meeting of the AMS and the RSME in Seville in the summer of 2003. We are very grateful to Bernd Sturmfels, for his thoughtful advice, and for directing us to the Cayley octads example in Subsection 6.4. Many thanks to Alicia Dickenstein for a very helpful discussion on resultants. Thanks also to Frank Sottile for productive conversations. We also wish to thank the anonymous referees for their valuable suggestions to improve this work. LFM was partially supported by NSF Grant DMS-1500832. BR was partially supported by Simons Collaboration Grant 280987. Publisher Copyright: {\textcopyright} 2021. Sociedade Portuguesa de Matem{\'a}tica Published by EMS Press.",
year = "2021",
doi = "10.4171/PM/2063",
language = "English (US)",
volume = "78",
pages = "129--146",
journal = "Portugaliae Mathematica",
issn = "0032-5155",
publisher = "European Mathematical Society Publishing House",
number = "2",
}