Stillman's conjecture via generic initial ideals

Draisma, Jan; Lason, Michael; Leykin, Anton (2019). Stillman's conjecture via generic initial ideals. Communications in algebra, 47(6), pp. 2384-2395. Taylor & Francis 10.1080/00927872.2019.1574806

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Using recent work by Erman–Sam–Snowden, we show that finitely generated ideals in the ring of bounded-degree formal power series in infinitely many variables have finitely generated Gröbner bases relative to the graded reverse lexicographic order. We then combine this result with the first author’s work on topological Noetherianity of polynomial functors to give an algorithmic proof of the following statement: ideals in polynomial rings generated by a fixed number of homogeneous polynomials of fixed degrees only have a finite number of possible generic initial ideals, independently of the number of variables that they involve and independently of the characteristic of the ground field. Our algorithm outputs not only a finite list of possible generic initial ideals, but also finite descriptions of the corresponding strata in the space of coefficients.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Draisma, Jan and Lason, Michael

Subjects:

500 Science > 510 Mathematics

ISSN:

0092-7872

Publisher:

Taylor & Francis

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

06 Aug 2019 13:49

Last Modified:

22 Oct 2019 21:14

Publisher DOI:

10.1080/00927872.2019.1574806

ArXiv ID:

1802.10139v2

BORIS DOI:

10.7892/boris.132252

URI:

https://boris.unibe.ch/id/eprint/132252

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