A divisor with nonclosed diminished base locus
A divisor with nonclosed diminished base locus

John Lesieutre , Massachusetts Institute of Technology
Fine Hall 322
I will explain the construction of a pseudoeffective Rdivisor Dλ on the blowup 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 Rdivisor which is nef on very general fibers of a family, but fails to be nef over countably many prime divisors in the base.