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NCTS Seminar in Algebraic Geometry
 
14:00 - 15:30, June 16, 2017 (Friday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Inequalities of Mobility Functions between the Cycle Classes and their Intersections with Divisors
Wei-Chung Chen (University of Tokyo)

Abstract

The volume of a Cartier divisor on a projective integral variety measures the asymptotic rate of growth of the dimension of the global sections of the multiples of the divisor. It provides a good way to understand the big divisor classes. As a generalization, the mobility defined on the cone of pseudo-effective cycle classes measures the asymptotic rate of growth of the dimensions of the global sections of the multiples of the cycle classes. It provides a way to understand the big cycle classes. The mobility function for divisors coincides with the volume function, and the mobility function for 0-cycles is just n! times the degree function deg. However, the mobility is difficult to compute in general. None of a non-trivial example of mobility is known precisely. The main purpose of this article is to provide an inequality between the mobility of a cycle class and its intersection with a nef divisor. Using this inequality, we can find an upper bound of the mobility of a cycle in terms of the degree of its intersection with divisors. 



 

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