Log Abundance for Kähler Threefolds

Omprokash Das, University of California, LA
Fine Hall 322


In a series of papers by Campana, Höring and Peternell, the authors established the K_X-MMP for terminal Kähler threefolds. They also proved the abundance conjecture in this settings. This is a remarkable achievement by the authors despite the fact that some of fundamental tools of MMP for algebraic varieties, such as, Mori’s Bend and Break, Base point free theorem etc. do not hold for Kähler manifolds. In this talk I will explain how to extend their K_X-abundance theorem to log canonical pairs (X, B), where X is a Kähler threefold and K_X+B is nef.