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Abstract:
I will describe work (partly in progress) on defining asymptotic
intersection numbers of big (or pseudoeffective) line bundles on smooth
projective varieties. Intuition is provided by intersecting with the
positive part of a Zariski decomposition, in case it exists. The technical
tool is a notion of volume for restrictions of linear series. One shows
that the asymptotic intersection numbers and the restricted volumes define
continuous functions of the big cone of the ambient variety, and obtain an
interesting decomposition of this cone given by their zero-locus. This is
joint work with Ein, Lazarsfeld, Mustata and Nakamaye.
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