Topological Abel-Jacobi Mapping and Jacobi Inversion

Hodge theory;Abel-Jacobi mapping;Jacobi inversion;Mathematics;Science;Mathematics

Zhao, XiaoleiMustata, Mircea ;

University of Michigan

关键词: Hodge theory;    Abel-Jacobi mapping;    Jacobi inversion;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/113505/xlzhao_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Intermediate Jacobian and Abel-Jacobi mapping play important roles in the study of cohomology classes and algebraic cycles of complex projective varieties. In this dissertation, we provide results in two directions. The first one is the construction of the topological Abel-Jacobi mapping, which is an extension of the classic Abel-Jacobi mapping, and satisfies a Jacobi inversion theorem. The other concerns the holomorphic Abel-Jacobi mapping, for which we give an alternate construction in the case of sufficiently ample hypersurfaces in any given smooth projective variety of even dimension.