主 题: Birational Geometry of Foliated Surfaces
报告人: Jihao Liu(University of Utah)
时 间: 2017-06-13 15:30 - 2017-06-13 16:30
地 点: Room 29, Quan Zhai, BICMR
\n\tIn this talk we will introduce and discuss the birational geometry of foliated surfaces. The\n<\/p>\n
\n\tpurpose of this talk is to show that we can run the minimal model program for foliated surfaces\n<\/p>\n
\n\t(with good singularities).\n<\/p>\n
\n\t1. We will review the preliminaries for foliated surfaces, e.g. denition of foliations, the canon-\n<\/p>\n
\n\tical divisor of a foliation, reduced singularities and canonical singularities of foliations.\n<\/p>\n
\n\t2. We will introduce some formulas for foliated surfaces, e.g. the intersection formulas, the\n<\/p>\n
\n\tCamacho-Sad formula.\n<\/p>\n
\n\t3. We will show how to run the KF-minimal model program of foliated surfaces.\n<\/p>\n
\n\t4. If we still have time we may introduce other related topics, e.g. the classication of foliations\n<\/p>\n
\n\tby their (numerical) Kodaira dimension, the failure of nite generation of the canonical ring of\n<\/p>\n
\n\tfoliations, the cone theorem\/partial MMP of high-dimensional foliations, etc.\n<\/p>\n
\n\tThe key references are the following:\n<\/p>\n
\n\t[Bru00] M.Brunella, Birational geometry of foliations, Monografas de Matematica, Instituto\n<\/p>\n
\n\tde Matematica Pura e Aplicada(IMPA), Rio de janeiro, 2000.\n<\/p>\n
\n\t[Bru02] M.Brunella, Foliations on complex projective surfaces, arXiv:math\/0212082, 2002, 31p.\n<\/p>\n
\n\t[McQ08] M.McQuillan, Canonical models of foliations. Pure Appl. Math. Q., 4(3, part 2),\n<\/p>\n
\n\t2008, pp. 877-1012.\n<\/p>
