PROPER REPARAMETRIZATION FOR INHERENTLY IMPROPER UNIRATIONAL VARIETIES

作     者：Liyong SHEN Engwee CHIONH Xiao-Shan GAO Jia LI 

作者机构：School of Mathematical Sciences Graduate University Chinese Academy of Sciences Beijing 100049 China School of Computing National University of Singapore 117543 Singapore. Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science ChineseAcademy of Sciences Beijing 100190 China. Beijing Electrical Science and Technology Institute Beijing 100070 China. 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2011年第24卷第2期

页      面：367-380页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 08[工学] 080401[工学-精密仪器及机械] 0815[工学-水利工程] 0804[工学-仪器科学与技术] 081503[工学-水工结构工程] 0811[工学-控制科学与工程] 081102[工学-检测技术与自动化装置] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：This research is supported by the National Key Basic Research Project of China under Grant No. 2011CB302400 and the National Natural Science Foundation of China under Grant No. 10901163 

主　　题：BKK bound chow form improper lattice supports improper rational parametrizations,reparametrization support transformation. 

摘      要：In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.