The minimal genus problem in rational surfaces CP^2#nCP^2  

作　　者：ZHAO Xu’an,GAO Hongzhu & QIU Huaidong LMAM,School of Mathematics Science, Beijing Normal University, Beijing 100875, China 

出　　处：《Science China Mathematics》2006年第9期1275-1283,共9页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.10371008);a grant of Jingshi Scholar of Beijing Normal University.

摘　　要：There are three key ingredients in the study of the minimal genus problem for rational surfaces CP2#nCP2: the generalized adjunction formula, the action of the orthogonal group of the Lorentz space and the geometric construction. In this paper, we prove the uniqueness of the standard form (see Definition 1.1 and Theorem 1.1) of a 2-dimensional homology class under the action of the subgroup of the Lorentz orthogonal group that is realized by the diffeomorphisms of CP2#nCP2.Using the geometric construction, we determine the minimal genera of some classes (see Theorem 1.2).

关 键 词：rational surfaces minimal genus Lorentz orthogonal transformation 

分 类 号：O189.1[理学—数学]