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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/197426
Connectedness Bertini Theorem via numerical equivalence
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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.
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MARTINELLI, Diletta, NARANJO DEL VAL, Juan Carlos and PIROLA, Gian Pietro. Connectedness Bertini Theorem via numerical equivalence. Advances in Geometry. 2017. Vol. 17, num. 1, pags. 31-38. ISSN 1615-715X. [consulted: 6 of October of 2026]. Available at: https://hdl.handle.net/2445/197426