Zhang Jia-jin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 60-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Configurations Of Points In P1 And Local Systems Of Rank One --- p.6 / Chapter 2.1 --- Configurations Of Points In P1 --- p.6 / Chapter 2.2 --- Local Systems Of Rank One --- p.7 / Chapter 2.3 --- Arithmeticity And Integral Monodromy --- p.12 / Chapter 3 --- Generalized Jacobians --- p.13 / Chapter 4 --- Stable Reductions Of Family Of Curves --- p.17 / Chapter 4.1 --- Normalization Of Cyclic Branched coverings --- p.17 / Chapter 4.2 --- Stable Reductions --- p.19 / Chapter 5 --- "Family Of n-th Cyclic Coverings Of P1, Abelian Va- rieties And CM-type" --- p.22 / Chapter 5.1 --- Family Of n-th Cyclic Coverings Of P1 --- p.22 / Chapter 5.2 --- Abelian Varieties And CM-type --- p.24 / Chapter 6 --- Families of Jacobians Coming From [6] --- p.27 / Chapter 6.1 --- Example 1. Family y3 = x(x ´ؤ l)(x ´ؤ λ)(x ´ؤμ) --- p.27 / Chapter 6.2 --- Example 2. Family y5=x(x ´ؤ l)(x ´ؤ λ)(x ´ؤμ) --- p.34 / Chapter 6.3 --- Other Families --- p.38 / Bibliography --- p.60

Huang Yong Dong. / Thesis submitted in: November 2003. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 59-60). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Abelian Varieties And Shimura Varieties --- p.5 / Chapter 1.2 --- Jacobians of Some Families of Curves --- p.7 / Chapter 1.3 --- Endomorphism Algebras of Jacobians of Curves --- p.8 / Chapter 2 --- Families of Abelian Varieties --- p.11 / Chapter 2.1 --- Abelian Varieties --- p.11 / Chapter 2.2 --- The Endomorphism Algebra of A Simple Abelian Varieties --- p.13 / Chapter 2.3 --- Family of Abelian Varieties and Shimura Varieties --- p.15 / Chapter 2.3.1 --- Real Multiplication --- p.16 / Chapter 2.3.2 --- Totally Indefinite Quaternion Multiplication --- p.19 / Chapter 2.3.3 --- Totally Definite Quaternion Multiplication --- p.22 / Chapter 2.3.4 --- Complex Multiplication --- p.25 / Chapter 2.3.5 --- Shimura Varieties --- p.28 / Chapter 2.4 --- The Endomorphism Algebra of A General Member --- p.29 / Chapter 3 --- Jacobians of Some Families of Curves --- p.32 / Chapter 3.1 --- Some Families of Curves --- p.32 / Chapter 3.2 --- Kodaira-Spencer Map --- p.37 / Chapter 3.3 --- Infinity of CM Type Points --- p.46 / Chapter 3.3.1 --- Φ Is Dominant --- p.46 / Chapter 3.3.2 --- Infinity of CM Points --- p.50 / Chapter 4 --- Endomorphism Algebras of Jacobians of Some Fam- ilies of Curves --- p.51 / Chapter 4.1 --- Jacobians Between Finite Coverings of Curves --- p.51 / Chapter 4.2 --- Endomorphism Algebras of Families of Jacobians --- p.53 / Chapter 4.2.1 --- The Case For μ = 1 --- p.53 / Chapter 4.2.2 --- The Case For μ = 2 --- p.55 / Chapter 4.2.3 --- The Case For μ =3 --- p.58 / Bibliography

published_or_final_version / abstract / toc / Mathematics / Doctoral / Doctor of Philosophy

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2008. / Includes bibliographical references (p. 45-46).

No description available.

There has been extensive research activities in the last couple of years to efficiently determine large sparse Jacobian matrices. It is now well known that the estimation of Jacobian matrices can be posed as a graph coloring problem. Unidirectional coloring by Coleman and More [9] and bidirectional coloring independently proposed by Hossain and Steihaug [23] and Coleman and Verma [12] are techniques that employ graph theoretic ideas. In this thesis we present heuristic and exact bidirectional coloring techniques. For bidirectional heuristic techniques we have implemented variants of largest first ordering, smallest last ordering, and incidence degree ordering schemes followed by the sequential algorithm to determine the Jacobian matrices. A "good" lower bound given by the maximum number of nonzero entries in any row of the Jacobian matrix is readily obtained in an unidirectional determination. However, in a bidirectional determination no such "good" lower bound is known. A significant goal of this thesis is to ascertain the effectiveness of the existing heuristic techniques in terms of the number of matrix-vector products required to determine the Jacobian matrix. For exact bidirectional techniques we have proposed an integer linear program to solve the bidirectional coloring problem. Part of exact bidirectional coloring results were presented at the "Second International Workshop on Cominatorial Scientific Computing (CSC05), Toulouse, France." / viii, 83 leaves ; 29 cm.

Thesis (M.S.)--Ohio University, August, 1998. / Title from PDF t.p.

Thesis (Ph. D.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 118-125).

Thesis (MSc)--University of Stellenbosch, 2005. / Bibliography. Also available via the Internet.

Doctor of Philosophy (PhD) / In this work, we investigate methods for computing explicitly with homomorphisms (and particularly endomorphisms) of Jacobian varieties of algebraic curves. Our principal tool is the theory of correspondences, in which homomorphisms of Jacobians are represented by divisors on products of curves. We give families of hyperelliptic curves of genus three, five, six, seven, ten and fifteen whose Jacobians have explicit isogenies (given in terms of correspondences) to other hyperelliptic Jacobians. We describe several families of hyperelliptic curves whose Jacobians have complex or real multiplication; we use correspondences to make the complex and real multiplication explicit, in the form of efficiently computable maps on ideal class representatives. These explicit endomorphisms may be used for efficient integer multiplication on hyperelliptic Jacobians, extending Gallant--Lambert--Vanstone fast multiplication techniques from elliptic curves to higher dimensional Jacobians. We then describe Richelot isogenies for curves of genus two; in contrast to classical treatments of these isogenies, we consider all the Richelot isogenies from a given Jacobian simultaneously. The inter-relationship of Richelot isogenies may be used to deduce information about the endomorphism ring structure of Jacobian surfaces; we conclude with a brief exploration of these techniques.