NORTHEASTERN
UNIVERSITY
MATHEMATICS
DEPARTMENT
REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
David Cox
(Amherst College)
Differentials in Tate Resolutions
ABSTRACT: The
Tate resolution of a coherent sheaf on projective space is a
bi-infinite exact complex over an exterior algebra. The modules
in the complex are known from the work of Eisenbud, Floystad and
Schreyer, but the differentials are only partially known. This
lecture will explore three aspects of these differentials. First,
for sheaves arising from Veronese embeddings, the Bezoutian gives one
choice for the differentials. Second, for sheaves arising from
Segre embeddings, the toric Jacobian (closely related to
hyperdeterminants in this case) gives a choice for the differentials,
though proving this requires some classical representation
theory. The third part of the lecture will consist of some
speculative remarks (work in progress) about the relation between Tate
resolutions and certain Weyman complexes. The second and third
parts of the lecture are based on joint work with E. Materov.
April 1, 2008
10:30 - 11:30
(Notice unusual day)
511
Lake Hall
For
further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html
or contact Alex Martsinkovsky alexmart >at< neu >dot< edu