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1998•Nagoya Mathematical JournalOpen access

Fano 4-Folds with scroll structure

Adrián Langer

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Abstract

Abstract. We classify smooth Fano 4-folds with second betti number b2 = 2, possesing adjunction theoretic scroll structure. These manifolds occur to be projectivisations of coherent sheaves over Fano manifolds. The paper deals mainly with projectivisations of non-locally free rank 2 Fano sheaves over Fano 3-folds with b2 = 1, using Mori theory. By the way, we classify nef and big rank 2 bundles over P2 with the first Chern class (3).

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Abstract. We classify smooth Fano 4-folds with second betti number b2 = 2, possesing adjunction theoretic scroll structure. These manifolds occur to be projectivisations of coherent sheaves over Fano manifolds. The paper deals mainly with projectivisations of non-locally free rank 2 Fano sheaves over Fano 3-folds with b2 = 1, using Mori theory. By the way, we classify nef and big rank 2 bundles over P2 with the first Chern class (3).

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Available abstract

Abstract. We classify smooth Fano 4-folds with second betti number b2 = 2, possesing adjunction theoretic scroll structure. These manifolds occur to be projectivisations of coherent sheaves over Fano manifolds. The paper deals mainly with projectivisations of non-locally free rank 2 Fano sheaves over Fano 3-folds with b2 = 1, using Mori theory. By the way, we classify nef and big rank 2 bundles over P2 with the first Chern class (3).

Key concepts: Adjunction, Fano plane, Mathematics, Scroll, Rank (graph theory), Pure mathematics, Chern class, Geometry

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