### Uittreksel

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. Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.

Taal | Engels |
---|---|

Pagina's | 2384-2395 |

Tijdschrift | Communications in Algebra |

Volume | 47 |

Nummer van het tijdschrift | 6 |

DOI's | |

Status | Gepubliceerd - 16 apr 2019 |

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### Trefwoorden

### Citeer dit

*Communications in Algebra*,

*47*(6), 2384-2395. DOI: 10.1080/00927872.2019.1574806

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*Communications in Algebra*, vol. 47, nr. 6, blz. 2384-2395. DOI: 10.1080/00927872.2019.1574806

**Stillman’s conjecture via generic initial ideals.** / Draisma, Jan; Lasoń, Michał; Leykin, Anton (Corresponding author).

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

TY - JOUR

T1 - Stillman’s conjecture via generic initial ideals

AU - Draisma,Jan

AU - Lasoń,Michał

AU - Leykin,Anton

PY - 2019/4/16

Y1 - 2019/4/16

N2 - 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. Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.

AB - 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. Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.

KW - Stillman's conjecture

UR - http://www.scopus.com/inward/record.url?scp=85064715884&partnerID=8YFLogxK

U2 - 10.1080/00927872.2019.1574806

DO - 10.1080/00927872.2019.1574806

M3 - Article

VL - 47

SP - 2384

EP - 2395

JO - Communications in Algebra

T2 - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 6

ER -