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The existence of equivariant pure free resolutions

David Eisenbud;  Gunnar Fløystad;  Jerzy Weyman — 2011

Annales de l’institut Fourier

Let A = K [ x 1 , ⋯ , x m ] be a polynomial ring in m variables and let d = ( d 0 < ⋯ < d m ) be a strictly increasing sequence of m + 1 integers. Boij and Söderberg conjectured the existence of graded A -modules M of finite length having pure free resolution of type d in the sense that for i = 0 , ⋯ , m the i -th syzygy module of M has generators only in degree d i . This paper provides a construction, in characteristic zero, of modules with this property that are also G L ( m ) -equivariant. Moreover, the construction works over...

Artin-Schelter regular algebras of dimension five

Gunnar Fløystad;  Jon Eivind Vatne — 2011

Banach Center Publications

We show that there are exactly three types of Hilbert series of Artin-Schelter regular algebras of dimension five with two generators. One of these cases (the most extreme) may not be realized by an enveloping algebra of a graded Lie algebra. This is a new phenomenon compared to lower dimensions, where all resolution types may be realized by such enveloping algebras.

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