Divisors in global analytic sets

  • Francesca Acquistapace

    Università degli Studi di Pisa, Italy
  • A. Díaz-Cano

    Universidad Complutense de Madrid, Spain

Abstract

We prove that any divisor of a global analytic set has a generic equation, that is, there is an analytic function vanishing on with multiplicity one along each irreducible component of . We also prove that there are functions with arbitrary multiplicities along . The main result states that if is pure dimensional, is locally principal, is not connected and represents the zero class in then the divisor is globally principal.

Cite this article

Francesca Acquistapace, A. Díaz-Cano, Divisors in global analytic sets. J. Eur. Math. Soc. 13 (2011), no. 2, pp. 297–307

DOI 10.4171/JEMS/253