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On a class of algebraic surfaces with numerically effective cotangent bundles
Wang, Hongyuan

2006, Doctor of Philosophy, Ohio State University, Mathematics.
In this dissertation, we will present two new results in complex geometry. The first one is for a borderline class of surfaces with nef cotangent bundle. The statement of the main theorem on this topic is as follows, suppose M is a general type surface, such that the two Chern numbers satisfy $c12=c2, and Pic(M)/Pic0(M) is generated by KM, then every nontrivial extension of the holomorphic tangent bundle TM by KM will be Hermitian flat. As a corollary, we obtain that every surface with the above described properties and with h1(TMKM*) > 0 will be a generalized theta divisor. The second result is an extended version of Hard Lefschetz theorem for the cohomology with values in Nakano semipositive vector bundles on a compact Kähler manifolds.
Fangyang Zheng (Advisor)

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Wang, H. (2006). On a class of algebraic surfaces with numerically effective cotangent bundles. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Wang, Hongyuan. "On a class of algebraic surfaces with numerically effective cotangent bundles." Electronic Thesis or Dissertation. Ohio State University, 2006. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Wang, Hongyuan "On a class of algebraic surfaces with numerically effective cotangent bundles." Electronic Thesis or Dissertation. Ohio State University, 2006. https://etd.ohiolink.edu/

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