Square-root Parametrization of Plane Curves

Shreeram S. Abhyankar

Chapter 2 in Algebraic Geometry and its Applications, 1994, pp 19-84 from Springer

Abstract: Abstract By calculating the genus of an irreducible algebraic plane curve of degree n in terms of its singularities, we see that, counted properly, the curve can have at most $$\frac{{(n - 1)(n - 2)}} {2}$$ double points, and it can be rationally parametrized iff this maximum is reached. If the maximum falls short by one or two, then the curve can still be parametrized by square-roots of rational functions. Such a square-root parametrization is used for factoring certain bivariate polynomials over a finite field.

Keywords: Galois Group; Double Point; Plane Curf; Hyperelliptic Curve; Splitting Field (search for similar items in EconPapers)
Date: 1994
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:978-1-4612-2628-4_2

Ordering information: This item can be ordered from
http://www.springer.com/9781461226284

DOI: 10.1007/978-1-4612-2628-4_2

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 ().