Metric contraction of the cone divisor by the conical K\'ahler-Ricci flow

Autor:	Edwards, Gregory
Rok vydání:	2017
Předmět:	Mathematics - Differential Geometry 53C44 (primary) 35K55 (secondary)
Druh dokumentu:	Working Paper
Popis:	We use the momentum construction of Calabi to study the conical K\"ahler-Ricci flow on Hirzebruch surfaces with cone angle along the exceptional curve, and show that either the flow Gromov-Hausdorff converges to the Riemann sphere or a single point in finite time, or the flow contracts the cone divisor to a single point and Gromov-Hausdorff converges to a two dimensional projective orbifold. This gives the first example of the conical K\"ahler-Ricci flow contracting the cone divisor to a single point. At the end, we introduce a conjectural picture of the geometry of finite time non-collapsing singularities of the flow on K\"ahler surfaces in general. Comment: 27 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1704.00360 Zobrazit plný text záznamu View this record from Arxiv