Partially positive line bundles

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• Totaro, B (DPMMS, Cambridge)
• Thursday 12 May 2011, 10:30-11:30
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact Mustapha Amrani.

Moduli Spaces

Define a line bundle L on a projective variety to be q-ample, for a natural number q, if tensoring with high powers of L kills coherent sheaf cohomology above dimension q. Thus 0-ampleness is the usual notion of ampleness. Intuitively, a line bundle is q-ample if it is positive “in all but at most q directions”.

We prove some of the basic properties of q-ample line bundles. Related ideas have been used by Ottem to define what an “ample subvariety” of any codimension should mean.

This talk is part of the Isaac Newton Institute Seminar Series series.

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