John Lesieutre : Counterexamples to some positivity questions

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Nov. 13, 2013, 4 p.m.

In

SEO 427

Abstract

I will explain the failure of several "positivity" properties of divisors: nefness is not an open condition in families; the diminished base locus of a divisor is not always a closed set; Zariski decompositions do not necessarily exist in dimension three; and asymptotic multiplicity invariants are not always finite in the relative setting.