Publication:
Divisors in global analytic sets

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http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=13&iss=2&rank=2&srch=searchterm%7CDivisors+in+global+analytic+sets
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2011
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European Mathematical Society
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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.
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Geometria algebraica
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1201.01 Geometría Algebraica
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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)
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https://hdl.handle.net/20.500.14352/42135
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