Relative linear extensions of sextic del Pezzo fibrations

2018/03/03 by Takeru Fukuoka, Fukuoka, Takeru · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.AG #msc:14E25 #msc:14E30

paper · pdf · doi:10.48550/arxiv.1803.01264

45 pages; abstract changed, exposition improved, references added

arxiv created 2018/09/22 · arxiv updated 2018/09/25

Abstract

In this paper, we study a sextic del Pezzo fibration over a curve comprehensively. We obtain certain formulae of several basic invariants of such a fibration. We also establish the embedding theorem of such a fibration which asserts that every such a fibration is a relative linear section of a Mori fiber space with the general fiber (ℙ¹)³ and that with the general fiber (ℙ²)². As an application of this embedding theorem, we classify singular fibers of such a fibrations and answer a question of T. Fujita about existence of non-normal fibers.

Cited by

• Refinement of the classification of weak Fano threefolds with sextic del Pezzo fibrations
• On compactifications of affine homology 3-cells into quadric fibrations

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