Stillman’s conjecture via generic initial ideals

Jan Draisma, Michał Lasoń, Anton Leykin (Corresponding author)

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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.

TaalEngels
Pagina's2384-2395
TijdschriftCommunications in Algebra
Volume47
Nummer van het tijdschrift6
DOI's
StatusGepubliceerd - 16 apr 2019

Vingerafdruk

Generic Initial Ideal
Finitely Generated
Lexicographic Order
Formal Power Series
Homogeneous Polynomials
Gröbner Basis
Polynomial ring
Functor
Reverse
Ring
Polynomial
Output
Coefficient

Trefwoorden

    Citeer dit

    Draisma, Jan ; Lasoń, Michał ; Leykin, Anton. / Stillman’s conjecture via generic initial ideals. In: Communications in Algebra. 2019 ; Vol. 47, Nr. 6. blz. 2384-2395
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    Stillman’s conjecture via generic initial ideals. / Draisma, Jan; Lasoń, Michał; Leykin, Anton (Corresponding author).

    In: Communications in Algebra, Vol. 47, Nr. 6, 16.04.2019, blz. 2384-2395.

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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    Draisma J, Lasoń M, Leykin A. Stillman’s conjecture via generic initial ideals. Communications in Algebra. 2019 apr 16;47(6):2384-2395. Beschikbaar vanaf, DOI: 10.1080/00927872.2019.1574806