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osu1291067498.pdf (401.98 KB)
ETD Abstract Container
Abstract Header
Geometry of general curves via degenerations and deformations
Author Info
Wang, Jie
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1291067498
Abstract Details
Year and Degree
2010, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
This thesis studies the geometric and deformational behavior of linear series under degenerations with the aim of attacking the maximal rank conjecture. There are three parts. The first part gives an explicit construction of the classical tangent-obstruction theory for deformations of the pair (
X,L
) to the case when
X
is local complete intersection scheme and
L
a line bundle on
X
. In the second part, we propose a new method, using deformation theory, to study the maximal rank conjecture. We prove that the maximal rank conjecture holds for the first unknown case: line bundles of extremal degree. Problems related to the maximal rank conjecture have become potentially accessible to this new method. In the third part, a canonical semi-stable degeneration of the
d
-th symmetric product
C
(
d
)
as the curve
C
becomes singular is constructed.
Committee
Herb Clemens (Advisor)
James Cogdell (Committee Member)
Roy Joshua (Committee Member)
Pages
81 p.
Subject Headings
Mathematics
Keywords
deformation of pairs
;
obstruction theory
;
maximal rank conjecture
;
line bundles of extremal degree
;
Hilbert scheme of points
Recommended Citations
Refworks
EndNote
RIS
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Citations
Wang, J. (2010).
Geometry of general curves via degenerations and deformations
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1291067498
APA Style (7th edition)
Wang, Jie.
Geometry of general curves via degenerations and deformations.
2010. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1291067498.
MLA Style (8th edition)
Wang, Jie. "Geometry of general curves via degenerations and deformations." Doctoral dissertation, Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1291067498
Chicago Manual of Style (17th edition)
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Document number:
osu1291067498
Download Count:
498
Copyright Info
© 2010, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.