Almost complete intersections and the Lex-Plus-Powers Conjecture
نویسنده
چکیده
We prove the almost complete intersection case of the Lex-Plus-Powers Conjecture on graded Betti numbers. We show that the resolution of a lex-plus-powers almost complete intersection provides an upper bound for the graded Betti numbers of any other ideal with regular sequence in the same degrees and the same Hilbert function. A key ingredient is finding an explicit comparison map between two Koszul complexes. Finally, we obtain bounds on the Hilbert function of an almost complete intersection, including a special case of a conjecture of Eisenbud-Green-Harris.
منابع مشابه
Ideals containing the squares of the variables
We study the Betti numbers of graded ideals containing the squares of the variables, in a polynomial ring. We prove the lex-plus-powers conjecture for such ideals.
متن کاملHilbert Schemes and Betti Numbers over a Clements-lindström Ring
We show that the Hilbert scheme, that parametrizes all ideals with the same Hilbert function over a Clements-Lindtröm ring W, is connected. More precisely, we prove that every graded ideal is connected by a sequence of deformations to the lex-plus-powers ideal with the same Hilbert function. Our result is an analogue of Hartshorne’s theorem that Grothendieck’s Hilbert scheme is connected; howev...
متن کاملConiveau 2 complete intersections and effective cones
The goal of this paper is first of all to propose a strategy to attack the generalized Hodge conjecture for coniveau 2 complete intersections, and secondly to state a conjecture concerning the cones of effective cycle classes in intermediate dimensions. Our main results show that the generalized Hodge conjecture for coniveau 2 complete intersections would follow from a particular case of this e...
متن کاملPowers of Complete Intersections: Graded Betti Numbers and Applications
Abstract. Let I = (F1, . . . , Fr) be a homogeneous ideal of the ring R = k[x0, . . . , xn] generated by a regular sequence of type (d1, . . . , dr). We give an elementary proof for an explicit description of the graded Betti numbers of Is for any s ≥ 1. These numbers depend only upon the type and s. We then use this description to: (1) write HR/Is , the Hilbert function of R/Is, in terms of HR...
متن کاملRaising to powers revisited
We consider the theory of algebraically closed fields of characteristic zero with raising to powers operations. In an earlier paper we have described complete first-order theories of such a structures, provided that a diophantine conjecture CIT does hold. Here we get rid of this assumption. The theory of complex numbers with raising to real powers satisfies the description if Schanuel’s conject...
متن کامل