On Classification of Higher-Dimensional Algebraic Varieties with Ample Vector Bundles

Zhi Yong CHEN, Fang Fang DENG

Acta Mathematica Sinica, Chinese Series ›› 2013, Vol. 56 ›› Issue (2) : 155-162.

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Acta Mathematica Sinica, Chinese Series ›› 2013, Vol. 56 ›› Issue (2) : 155-162. DOI: 10.12386/A2013sxxb0016
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On Classification of Higher-Dimensional Algebraic Varieties with Ample Vector Bundles

  • Zhi Yong CHEN1, Fang Fang DENG2
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Abstract

Let X be a smooth projective variety of dimension n(n≥3) and ε an ample vector bundle with rank r=n-k(k≥1) over X. We denote Λ(ε,KX)=max{(-KX-c1(ε))·C|R=R+[C]∈Ω, and l(R)=-KX·C}, where KX is the canonical bundle of X, c1(ε) means the first Chern class of ε, Ω denotes the set of extremal rays R such that (KX+c1(ε))·C≤0, R+ is the set of positive real number, and l(R) is the length of R. The classification of (X, ε) will ba given when Λ(ε,KX)≥k-1.

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ample vector bundles / higher-dimensional algebraic varieties / numerically effective

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Zhi Yong CHEN, Fang Fang DENG. On Classification of Higher-Dimensional Algebraic Varieties with Ample Vector Bundles. Acta Mathematica Sinica, Chinese Series, 2013, 56(2): 155-162 https://doi.org/10.12386/A2013sxxb0016

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