Fano manifolds with many free divisors
type: Item
instance of: scholarly article
title: Fano manifolds with many free divisors
zbMATH Open document ID: 1502.14094
author: Kento Fujita
published in: European Journal of Mathematics
publication date: 2022-10-21T00:00:00Z
review text: Let \(X\) be an \(n\)-dimensional Fano manifold. Let \(r\) be the index of \(X\), \(\rho\) the Picard number of \(X\) and \(L_X\) the line bundle such that \(rL \cong -K_X\). Motivated by a conjecture of Mukai the author proves several theorem with as a thesis that \(X\) is a multiprojective space (with factors of prescribed dimensions) and with as assumptions the existence of ``many'' free divisors. For instance, it is proved that if there exists \(\rho\) non-trivial free divisors \(D_1,\dots ,D_\rho\) with \(D_1+\cdots +D_\rho \in |L_X|\), then \(X \cong (\mathbb {P}^{r-1})^\rho\).
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14J45
Mathematics Subject Classification ID: 14E30
zbMATH DE Number: 7604897
zbMATH Keywords: Fano manifold
zbMATH Keywords: Mukai conjecture
zbMATH Keywords: extremal ray
zbMATH Keywords: multiprojective space
MaRDI profile type: Publication
full work available at URL: s40879-022-00559-z
OpenAlex ID: W4285800234
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DOI: 10.1007/S40879-022-00559-Z
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description: scientific article; zbMATH DE number 7604897