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Fano manifolds obtained by blowing up along curves with maximal Picard number

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Abstract

The Picard number of a Fano manifold X obtained by blowing up a curve in a smooth projective variety is known to be at most 5, in any dimension greater than or equal to 4. In this note, we show that the Picard number attains to the maximal if and only if X is the blow-up of the projective space whose center consists of two points, the strict transform of the line joining them and a linear subspace or a hyperquadric of codimension 2. This result is obtained as a consequence of a classification of special types of Fano manifolds.

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  1. Faculty of Liberal arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku Sakai, Osaka, 599-8531, Japan

    Toru Tsukioka

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  1. Toru Tsukioka
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Correspondence to Toru Tsukioka.

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Tsukioka, T. Fano manifolds obtained by blowing up along curves with maximal Picard number. manuscripta math. 132, 247–255 (2010). https://doi.org/10.1007/s00229-010-0346-4

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  • DOI: https://doi.org/10.1007/s00229-010-0346-4

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