# A divisor with non-closed diminished base locus

Tuesday, February 19, 2013 -

4:30pm to 6:00pm

I will explain the construction of a pseudoeffective R-divisor Dλ on the blow-up of P3 at nine very general points which has negative intersections with an infinite set of curves, whose union is Zariski dense. It follows that the diminished base locus B-(Dλ) = ∪A ample B(Dλ+A) is not closed and that Dλ does not admit a Zariski decomposition in even a very weak sense. Along the way I will discuss some related examples, including an 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.

Speaker:

John Lesieutre

Massachusetts Institute of Technology

Event Location:

Fine Hall 322