Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Jian Xiao, Tsinghua Yau Mathematical Sciences Center
Inviter:
Title:
Local positivity for curves
Time & Venue:
2018.10.17 10:45-11:45 N913
Abstract:
One of the most important invariants measuring the local positivity of a nef line bundle is the Seshadri constant. We first give a brief introduction to this invariant. Then using the duality of positive cones, we show that applying the polar transform to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants, studied also independently by M. Fulger, have nice properties similar to those for divisors. In particular, this enables us to obtain a Seshadri type ampleness criterion for movable curves, and give a characterization of the divisorial components of the non-ample locus of a big class. (Joint work with N. McCleerey.)