Complex manifolds whose blow-up at a point is Fano

DOI10.1016/S1631-073X(02)02284-7zbMath1036.14020MaRDI QIDQ1600138

Frédéric Campana, Jarosław A. Wiśniewski, Laurent Bonavero

Publication date: 8 September 2002

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

birational geometryample anticanonical bundleprojective blow-up

Mathematics Subject Classification ID

Fano varieties (14J45) Minimal model program (Mori theory, extremal rays) (14E30)

Related Items (17)

Fano varieties with large Seshadri constants ⋮ On Fano manifolds with a birational contraction sending a divisor to a curve ⋮ Characterization of projective spaces by Seshadri constants ⋮ Fano 4-folds, flips, and blow-ups of points ⋮ Classification of Fano manifolds containing a negative divisor isomorphic to projective space ⋮ The Lefschetz defect of Fano varieties ⋮ Unnamed Item ⋮ A conjecture of Mukai relating numerical invariants of Fano manifolds ⋮ On the minimal length of extremal rays for Fano four-folds ⋮ Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one ⋮ Generalized Mukai conjecture for special Fano varieties ⋮ Del Pezzo surface fibrations obtained by blow-up of a smooth curve in a projective manifold ⋮ A remark on Fano 4-folds having \((3,1)\)-type extremal contractions ⋮ Fano fivefolds of index two with blow-up structure ⋮ On weak Fano manifolds with small contractions obtained by blow-ups of a product of projective spaces ⋮ On a generalization of the Mukai conjecture for Fano fourfolds ⋮ Towards a criterion for slope stability of Fano manifolds along divisors

Cites Work

• Unnamed Item
• Unnamed Item
• On extremal rays of the higher dimensional varieties
• Two theorems on elementary contractions
• The adjunction theory of complex projective varieties
• Toward the classification of higher-dimensional toric Fano varieties
• Toric varieties whose blow-up at a point is Fano
• On the birational geometry of toric Fano -folds
• Torification and factorization of birational maps
• On contractions of extremal rays of Fano manifolds.

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