# Counterexamples to some positivity questions

## John Lesieutre (MIT)

I will explain the failure of some positivity properties of divisors: nefness is not an open condition in families over $\mathbb C$; the diminished base locus of a divisor is not always a closed set; Zariski decompositions do not always exist in dimension three, even in a weak sense; and asymptotic multiplicity invariants can be infinite in the relative setting. The examples are fairly elementary, arising on blow-ups of $\mathbb P^2$ and $\mathbb P^3$ at several points, and on certain Calabi-Yau threefolds.

Tuesday, October 8th, at 4:00pm in HBH 227

Return to talks from Fall 2013