|
Abstract:
Let d1,...,dn be a strictly increasing sequence of
integers. Boij and Söderberg [arXiv:math/0611081] have conjectured
the existence of a graded module M of finite length over any
polynomial ring K[x_1,..., x_n], whose minimal free resolution is
pure of type (d1,...,dn), in the sense that its i-th syzygies are
generated in degree di.
In this talk I will describe the proof of this conjecture when K is a field of
characteristic 0 by describing an Artinian, GL(n)-equivariant module
and its pure resolution, which is of the desired type.
The construction uses Bott's Theorem and the combinatorics of Schur
functors.
I will also discuss other conjectures of Boij and Söderberg on
Betti numbers of finite length modules. This is a joint work with D.Eisenbud and G. Floystad.
Reference: ArXiv 0709.1529.
|