Effective behavior of multiple linear systems
 

Shengli TAN
East China Normal U., China
 
 
 

Abstract

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Effective versions of some theorems in algebraic geometry have attracted much attention, for example, Fujita's conjecture and Matsusaka's big theorem. In this talk, I would like to present optimal effective bounds for some other well-known theorems on an algebraic surface X, which are respectively due to Zariski (1962), Castelnuovo (1897), Artin (1962, 1966), Benveniste (1984), Cutkosky and Srinivas (1993) and Serre. These theorems are about Riemann-Roch problem, vanishing theorems, base-point freeness and very ampleness of multiple linear systems.