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As an application of the theory of Lawson homology and morphic cohomology, Walker proved that the Abel-Jacobi map factors through another regular homomorphism. In this note, we give a direct proof of the theorem.
We construct a map between Blochs higher Chow groups and Deligne homology for smooth, complex quasiprojective varieties on the level of complexes. For complex projective varieties this results in a formula which generalizes at the same time the class
For a smooth projective variety $X$ of dimension $2n-1$, Zhao defined topological Abel-Jacobi map, which sends vanishing cycles on a smooth hyperplane section $Y$ of $X$ to the middle dimensional primitive intermediate Jacobian of $X$. When the vanis
In this paper, we show that there are solutions of every degree $r$ of the equation of Pell-Abel on some real hyperelliptic curve of genus $g$ if and only if $ r > g$. This result, which is known to the experts, has consequences, which seem to be unk
This work discovers the equivalence relation between quadrilateral meshes and meromorphic quartic. Each quad-mesh induces a conformal structure of the surface, and a meromorphic differential, where the configuration of singular vertices correspond to
This work proposes a rigorous and practical algorithm for generating meromorphic quartic differentials for the purpose of quad-mesh generation. The work is based on the Abel-Jacobi theory of algebraic curve. The algorithm pipeline can be summarized a