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Background on Curves and Jacobians
2005This chapter introduces the main characters of this book — curves and their Jacobians. To this aim we give a brief introduction to algebraic and arithmetic geometry. We first deal with arbitrary varieties and abelian varieties to give the general definitions in a concise way.
Frey, G., Lange, T.
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Compactification of generalised Jacobians
Proceedings of the Indian Academy of Sciences - Section A. Part 3, Mathematical Sciences, 1979The aim of this paper is to show that there is a natural “compactification” of the Picard Scheme of a Family of Curves and to study its properties.
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Algebraic Curves and Their Jacobians
1998The present paper gives a survey on the recent achievements in the theory of complex algebraic curves and their Jacobians. It focuses on four selected topics which have been in the center of interest during the past fifteen years, and in which the probably most remarkable progress has been made.
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Tying together the analytic Jacobian and algebraic Jacobian
2007So far in this Chapter, we have defined an algebraic variety Jac C and studied its invariant flows. In Chapter II, we associated to any compact Riemann Surface C a complex torus Jac C. If C is hyperelliptic so that both constructions apply, they are isomorphic by Abel’s theorem.
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Implicit function theorem and Jacobians in solvation and adsorption
Physica A: Statistical Mechanics and Its Applications, 2021Nobuyuki Matubayasi, Seishi Shimizu
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Decomposing Jacobians Via Galois covers
Experimental Mathematics, 2023Elisa Lorenzo Garcia +2 more
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Compactified Jacobians and q,t-Catalan numbers, I
Journal of Combinatorial Theory - Series A, 2013Eugene Gorsky, Mikhail Mazin
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Determinant Expansions of Signed Matrices and of Certain Jacobians
SIAM Journal on Matrix Analysis and Applications, 2009Raúl Gomez +2 more
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