316 research outputs found
A recollement of vector bundles
For a weighted projective line, the stable category of its vector bundles
modulo lines bundles has a natural triangulated structure. We prove that, for
any positive integers and with , there is an explicit
recollement of the stable category of vector bundles on a weighted projective
line of weight type relative to the ones on weighted projective
lines of weight types and
Bounds on cohomological support varieties
Over a local ring , the theory of cohomological support varieties attaches
to any bounded complex of finitely generated -modules an algebraic
variety that encodes homological properties of . We give lower
bounds for the dimension of in terms of classical invariants of .
In particular, when is Cohen-Macaulay and not complete intersection we find
that there are always varieties that cannot be realized as the cohomological
support of any complex. When has finite projective dimension, we also give
an upper bound for in terms of the dimension of the radical of
the homotopy Lie algebra of . This leads to an improvement of a bound due to
Avramov, Buchweitz, Iyengar, and Miller on the Loewy lengths of finite free
complexes. Finally, we completely classify the varieties that can occur as the
cohomological support of a complex over a Golod ring.Comment: 23 pages. Comments welcom
The adjoint of an even size matrix factors
We show that the adjoint matrix of a generic square matrix of even size can
be factored nontrivially, answering a question of G. Bergman. This note is a
preliminary report on work in progress.Comment: 7 pages, preliminary versio
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