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

Details The sharp lower bound for the volume of 3-folds of general type with χ(\Co{X})=1 The sharp lower bound for the volume of 3-folds of general type with χ(\Co{X})=1

2007-10-24

arxiv.org/abs/0710.4409v1

Mathematics

Algebraic Geometry

27 pages

Scientific paper

Let $V$ be a smooth projective 3-fold of general type. Denote by $K^{3}$, a
rational number, the self-intersection of the canonical sheaf of any minimal
model of $V$. One defines $K^{3}$ as a canonical volume of $V$. The paper is
devoted to proving the sharp lower bound $K^{3}\ge {1/420}$ which can be
reached by an example: $X_{46}\subseteq \mathbb{P}(4,5,6,7,23)$.

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