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osu1154450131.pdf (331.99 KB)
ETD Abstract Container
Abstract Header
On a class of algebraic surfaces with numerically effective cotangent bundles
Author Info
Wang, Hongyuan
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1154450131
Abstract Details
Year and Degree
2006, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
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 $c
1
2
=c
2
, and
Pic(M)/Pic
0
(M)
is generated by
K
M
, then every nontrivial extension of the holomorphic tangent bundle
T
M
by
K
M
will be Hermitian flat. As a corollary, we obtain that every surface with the above described properties and with
h
1
(
T
M
⊗
K
M
*
) > 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.
Committee
Fangyang Zheng (Advisor)
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Citations
Wang, H. (2006).
On a class of algebraic surfaces with numerically effective cotangent bundles
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1154450131
APA Style (7th edition)
Wang, Hongyuan.
On a class of algebraic surfaces with numerically effective cotangent bundles.
2006. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1154450131.
MLA Style (8th edition)
Wang, Hongyuan. "On a class of algebraic surfaces with numerically effective cotangent bundles." Doctoral dissertation, Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1154450131
Chicago Manual of Style (17th edition)
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Document number:
osu1154450131
Download Count:
1,952
Copyright Info
© 2006, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.