Notes on very ample vector bundles on 3-folds

2005/01/26 by Hidetoshi Maeda, Maeda, Hidetoshi, Andrew Sommese +1
Mathematics · #14J60 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14J60

paper · pdf · doi:10.48550/arxiv.math/0501471

12 pages

arxiv created 2005/01/26 · openalex publication_date 2005/01/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Cal E be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of \Cal E is provided when K_X+det \Cal E is nef but not big, and when a suitable positive multiple of K_X+det \Cal E defines a morphism X→ B with connected fibers onto a smooth projective curve B, where K_X is the canonical bundle of X. As an application, the case where the genus of B is positive and \Cal E has a global section whose zero locus is a smooth hyperelliptic curve of genus ≥ 2 is investigated, and our previous result is improved for threefolds.

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