The sharp lower bound for the volume of 3-folds of general type with χ(\CoX)=1

2007/10/24 by Lei Zhu, Zhu, Lei
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.0710.4409

27 pages

arxiv created 2007/10/24 · arxiv updated 2009/12/01

Abstract

Let V be a smooth projective 3-fold of general type. Denote by K³, a rational number, the self-intersection of the canonical sheaf of any minimal model of V. One defines K³ as a canonical volume of V. The paper is devoted to proving the sharp lower bound K³≥ 1/420 which can be reached by an example: X₄₆⊆ ℙ(4,5,6,7,23).

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