A study on the dimension of global sections of multiple adjoint bundle of polarized manifolds

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540043
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kochi University
• Principal Investigator: Fukuma Yoshiaki 高知大学, 自然科学系理学部門, 教授 (20301319)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 代数学 / 偏極多様体 / 準偏極多様体 / 豊富な因子 / nefかつbigな因子 / 随伴束 / 断面不変量

Outline of Final Research Achievements

In this research, we studied the minimal value m(n) which satisfies the following property: the dimension of global section of m(K+L) is positive for any n-dimensional quasi-polarized manifolds (X,L) and every integer m which is greater than or equal to m(n), where K denotes the canonical divisor of X. Then we proved that m(n) is less than or equal to 2n-4. Moreover for the case of 4-dimensional polarized manifolds, we proved a conjecture which was proposed by Beltrametti and Sommese. Furthermore I studied the sectional genus and the sectional class, which are invariants of polarized manifolds, and I got several results which have been unknown.

Free Research Field

代数幾何学