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Abstract:
This is a longstanding problem in Algebraic Geometry which has its roots in an
old paper by Horrocks where he proved that a vector bundle on a projective space
decomposes into a sum of line bundles iff it has no intermediate cohomology. I
will start my talk giving an easy and short proof of this result, which uses as a
main tool Beilinson's spectral sequence.
In the second part of my talk I will generalize Beilinson's spectral sequence
for vector bundles on projective spaces to vector bundles on other projective
varieties and I will use this generalization to extend Horrocks Theorem to
vector bundles on multiprojective spaces and to Steiner bundles on projective
varieties.
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