Monodromy and normal forms

Fabrizio Catanese
Additional contact information
Fabrizio Catanese: Universität Bayreuth, Mathematisches Institut

Chapter 6 in Karl Weierstraß (1815–1897), 2016, pp 195-218 from Springer

Abstract: Abstract We discuss the history of the monodromy theorem, starting from Weierstraß, and the concept of a monodromy group. From this viewpoint we compare then the Weierstraß, the Legendre and other normal forms for elliptic curves, explaining their geometric meaning and distinguishing them by their stabilizer in ℙSL(2, ℤ) and their monodromy. Then we focus on the birth of the concept of the Jacobian variety, and the geometrization of the theory of Abelian functions and integrals. We end illustrating the methods of complex analysis in the simplest issue, the difference equation f(z) = g(z + 1) - g(z) on ℂ.

Keywords: Normal Form; Analytic Continuation; Meromorphic Function; Elliptic Curve; Elliptic Curf (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-658-10619-5_7

Ordering information: This item can be ordered from
http://www.springer.com/9783658106195

DOI: 10.1007/978-3-658-10619-5_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().