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On the second sectional H-arithmetic genus of polarized manifolds

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Let (X,L) be a polarized variety defined over the complex number field with dim X=n. In this paper we introduce the notion of the i-th sectional H-arithmetic genus χH i (X,L) for every integer i with 0≤i≤n. We expect that this invariant has a property similar to the Euler-Poincaré characteristic of the structure sheaf of i-dimensional varieties. In this paper, we consider the case where X is smooth and i=2, and we study a polarized version of some results in the theory of surfaces.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kochi University, Akebono-cho, Kochi, 780-8520, Japan

    Yoshiaki Fukuma

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  1. Yoshiaki Fukuma
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Correspondence to Yoshiaki Fukuma.

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Mathematics Subject Classification (2000): 14C20, 14C17, 14C40, 14J29, 14J30, 14J35, 14J40

This research was partially supported by the Grant-in-Aid for Young Scientists (B) (No.14740018), The Ministry of Education, Culture, Sports, Science and Technology, Japan.

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Fukuma, Y. On the second sectional H-arithmetic genus of polarized manifolds. Math. Z. 250, 573–597 (2005). https://doi.org/10.1007/s00209-005-0766-0

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