A Module-theoretic Characterization of Algebraic Hypersurfaces
| Autor: | Cleto B. Miranda-Neto |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Algebraic cycle
Pure mathematics Hypersurface Function field of an algebraic variety General Mathematics Algebraic surface ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Real algebraic geometry Algebraic variety Dimension of an algebraic variety Divisor (algebraic geometry) GeneralLiterature_REFERENCE(e.g. dictionaries encyclopedias glossaries) Mathematics |
| Zdroj: | Canadian Mathematical Bulletin. 61:166-173 |
| ISSN: | 1496-4287 0008-4395 |
| DOI: | 10.4153/cmb-2016-099-6 |
| Popis: | In this note we prove the following surprising characterization: if X ⊂ is an (embedded, non-empty, proper) algebraic variety deûned over a field k of characteristic zero, then X is a hypersurface if and only if the module of logarithmic vector fields of X is a reflexive -module. As a consequence of this result, we derive that if is a free -module, which is shown to be equivalent to the freeness of the t-th exterior power of for some (in fact, any) t ≤ n, then necessarily X is a Saito free divisor. |
| Databáze: | OpenAIRE |
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