Generalizations of Stillman's Conjecture via Twisted Commutative Algebra. (19th August 2019)

• Record Type: Journal Article
• Authors: Erman, Daniel; Sam, Steven V; Snowden, Andrew
• Is Part Of: International mathematics research notices. Volume 2021:Number 16(2021)
• Page Start: 12281
• Page End: 12304
• Publication Date: 2019-08-19
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnz123
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: Combining recent results on Noetherianity of twisted commutative algebras by Draisma and the resolution of Stillman's conjecture by Ananyan–Hochster, we prove a broad generalization of Stillman's conjecture. Our theorem yields an array of boundedness results in commutative algebra that only depend on the degrees of the generators of an ideal and not the number of variables in the ambient polynomial ring.