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 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 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 کاملCurves on Threefolds and a Conjecture of Griffiths-harris
We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface X ⊂ P of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in P. We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group.
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: Proceedings of the American Mathematical Society
سال: 2014
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2014-12216-7