Acquistapace , Francesca and Díaz-Cano Ocaña, Antonio (2011) Divisors in global analytic sets. Journal of the European Mathematical Society, 13 (2). pp. 297-307. ISSN 1435-9855
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We prove that any divisor Y of a global analytic set X subset of R(n) has a generic equation, that is, there is an analytic function vanishing on Y with multiplicity one along each irreducible component of Y. We also prove that there are functions with arbitrary multiplicities along Y. The main result states that if X is pure dimensional, Y is locally principal, X \ Y is not connected and Y represents the zero class in H(q-1)(infinity) (X, Z(2)) then the divisor Y is globally principal.
|Uncontrolled Keywords:||Real analytic sets; Divisors|
|Subjects:||Sciences > Mathematics > Algebraic geometry|
Acquistapace, F., Broglia, F.: More about signatures and approximation. Geom. Dedicata 50, 107–116 (1994)
Acquistapace, F., Broglia, F., Tognoli, A.: Sulla normalizzazione degli spazi analitici reali. Boll. Un. Mat. Ital. (4) 12, 26–36 (1975)
|Deposited On:||24 Apr 2012 13:35|
|Last Modified:||14 May 2013 15:29|