A note on the classification of Fano manifolds of middle index
type: Item
instance of: scholarly article
title: A note on the classification of Fano manifolds of middle index
zbMATH Open document ID: 1083.14047
author: Gianluca Occhetta
published in: Manuscripta Mathematica
publication date: 2005-06-13T00:00:00Z
review text: In the classification of Fano manifolds of middle index, that is manifolds \(X\) of index \(r\) and \(\dim X = 2r\), the case of a Fano manifold of dimension \(6\), index \(3\) and Picard number two whose extremal contractions are \({\mathbb P}^{2}\)-bundles was a doubtful case. In the paper under review the author rules out such a case by studying unsplit families of rational curves. See [\textit{J. A. Wiśniewski} in: Projective geometry with applications, Lect. Notes Pure Appl. Math. 166, 19--26 (1994; Zbl 0839.14032)] for an account on Fano manifolds of middle index and \(b_{2}\geq 2\).
reviewed by: Maria Lucia Fania
Mathematics Subject Classification ID: 14J45
Mathematics Subject Classification ID: 14J40
zbMATH DE Number: 2175527
zbMATH Keywords: unsplit family of rational curves
MaRDI profile type: Publication
full work available at URL: s00229-005-0540-y
OpenAlex ID: W2022296812
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DOI: 10.1007/S00229-005-0540-Y
description: scientific article; zbMATH DE number 2175527