On stabilizers of algebraic function fields of one variable

Wulf Dieter Geyer, Moshe Jarden, Aharon Razon

Research output: Contribution to journalArticlepeer-review

Abstract

Let K be a fixed algebraic closure of an infinite field K. We consider an absolutely integral curve Γ in PKn PKn with n ≥ 2. The curve ΓKΓK should have only finitely many inflection points, finitely many double tangents, and there exists no point in PKnPKn through which infinitely many tangents to ΓKΓK go. In addition there exists a prime number q such that ΓKΓK has a cusp of multiplicity q and the multiplicities of all other points of ΓKΓK are at most q. Under these assumptions, we construct a non-empty Zariski-open subset O of PKnPKn such that if n ≥ 3, the projection from each point o O(K) birationally maps Γ onto an absolutely integral curve Γ in PKn-1 PKn-1 with the same properties as Γ (keeping q unchanged). If n = 2, then the projection from each o O(K) maps Γ onto PK1PK1 and leads to a stabilizing element t of the function field F of Γ over K. The latter means that F/K(t) is a finite separable extension whose Galois closure FF is regular over K.

Original languageEnglish
Pages (from-to)131-174
Number of pages44
JournalAdvances in Geometry
Volume17
Issue number2
DOIs
StatePublished - 1 Mar 2017

Keywords

  • Function feld
  • absolutely integral curve

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