Date: Wednesday, March 27, 2013
Location: 3088 East Hall (4:00 PM to 6:00 PM)
Title: A divisor with non-closed diminished base locus
Abstract:
I will explain the construction of a pseudoeffective $\mathbb R$-divisor $D$ on the blow-up of $\mathbb P^3$ at nine very general points which has negative intersections with a Zariski dense set of curves. The diminished base locus $\mathbf B_-(D) = \bigcup_{\text{$A$ ample}} \mathbf B(D+A)$ of $D$ is not closed, and $D$ does not admit a Zariski decomposition in even a very weak sense. By a similar method, I'll exhibit an $\mathbb R$-divisor which is nef on very general fibers of a family, but fails to be nef over countably many prime divisors in the base. I'll also discuss some related issues for divisors on Calabi-Yau threefolds.
Speaker: John Lesieutre
Institution: MIT
Event Organizer:
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