The Eisenbud-Green-Harris conjecture for fast-growing degree sequences
نویسندگان
چکیده
Let $S$ be a standard graded polynomial ring over field, and $I$ homogeneous ideal that contains regular sequence of degrees $d_1,\ldots,d_n$. We prove the Eisenbud-Green-Harris conjecture when forms satisfy $d_i \geqslant \sum_{j=1}^{i-1}(d_j-1)$, improving result obtained in 2008 by first author Maclagan. Except for sporadic case five quadrics, recently proved Gunturkun Hochster, results this article recover all known cases where only are fixed, include several additional ones.
منابع مشابه
Some Cases of the Eisenbud-green-harris Conjecture
The Eisenbud-Green-Harris conjecture states that a homogeneous ideal in k[x1, . . . , xn] containing a homogeneous regular sequence f1, . . . , fn with deg(fi) = ai has the same Hilbert function as an ideal containing xi i for 1 ≤ i ≤ n. In this paper we prove the Eisenbud-Green-Harris conjecture when aj > ∑j−1 i=1 (ai −1) for all j > 1. This result was independently obtained by the two authors.
متن کاملCounterexamples to the Eisenbud-goto Regularity Conjecture
Abstract. Our main theorem shows that the regularity of non-degenerate homogeneous prime ideals is not bounded by any polynomial function of the degree; this holds over any field k. In particular, we provide counterexamples to the longstanding Regularity Conjecture, also known as the Eisenbud-Goto Conjecture (1984). We introduce a method which, starting from a homogeneous ideal I, produces a pr...
متن کاملA Special Case of the Buchsbaum-eisenbud-horrocks Rank Conjecture
The Buchsbaum-Eisenbud-Horrocks rank conjecture proposes lower bounds for the Betti numbers of a graded module M based on the codimension of M . We prove a special case of this conjecture via Boij-Söderberg theory. More specifically, we show that the conjecture holds for graded modules where the regularity of M is small relative to the minimal degree of a first syzygy of M . Our approach also y...
متن کاملThe Eisenbud - Koh - Stillman Conjecture on Linear Syzygies
Although the relationship between minimal free resolutions and Koszul cohomology has been known for a long time, it has been difficult to find a way to fully utilize the " exterior " nature of the Koszul classes. The technique used here seems to be one way to begin to do this. We prove a conjecture of Eisenbud-Koh-Stillman on linear syzygies and in consequence a conjecture of Lazarsfeld and mys...
متن کاملOn a Conjecture by Kalai
We show that monomial ideals generated in degree two satisfy a conjecture by Eisenbud, Green and Harris. In particular we give a partial answer to a conjecture of Kalai by proving that h-vectors of flag Cohen-Macaulay simplicial complexes are h-vectors of Cohen-Macaulay balanced simplicial complexes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annali della Scuola normale superiore di Pisa. Classe di scienze
سال: 2023
ISSN: ['0391-173X', '2036-2145']
DOI: https://doi.org/10.2422/2036-2145.202203_025