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http://hdl.handle.net/2445/197426
Title: | Connectedness Bertini Theorem via numerical equivalence |
Author: | Martinelli, Diletta Naranjo del Val, Juan Carlos Pirola, Gian Pietro |
Keywords: | Geometria algebraica Superfícies algebraiques Algebraic geometry Algebraic surfaces |
Issue Date: | 8-Jan-2017 |
Publisher: | Walter de Gruyter |
Abstract: | Let $X$ be an irreducible projective variety and let $f: X \rightarrow \mathbb{P}^n$ be a morphism. We give a new proof of the fact that the preimage of any linear variety of dimension $k \geq n+1-\operatorname{dim} f(X)$ is connected. We show that the statement is a consequence of the Generalized Hodge Index Theorem using easy numerical arguments that hold in any characteristic. We also prove the connectedness Theorem of Fulton and Hansen as an application of our main theorem. |
Note: | Reproducció del document publicat a: https://doi.org/10.1515/advgeom-2016-0028 |
It is part of: | Advances in Geometry, 2017, vol. 17, num. 1, p. 31-38 |
URI: | http://hdl.handle.net/2445/197426 |
Related resource: | https://doi.org/10.1515/advgeom-2016-0028 |
ISSN: | 1615-715X |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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647362.pdf | 659 kB | Adobe PDF | View/Open |
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