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The Ohio State University

1. Wang, Jie. Geometry of general curves via degenerations and deformations.

Degree: PhD, Mathematics, 2010, The Ohio State University

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 (<i>X,L</i>) to the case when <i>X</i> is local complete intersection scheme and <i>L</i> a line bundle on <i>X</i>. 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 <i>d</i>-th symmetric product <i>C</i><sup>(<i>d</i>)</sup> as the curve <i>C</i> becomes singular is constructed. Advisors/Committee Members: Clemens, Herb (Advisor).

Subjects/Keywords: Mathematics; deformation of pairs; obstruction theory; maximal rank conjecture; line bundles of extremal degree; Hilbert scheme of points

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Wang, J. (2010). Geometry of general curves via degenerations and deformations. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1291067498

Chicago Manual of Style (16th Edition):

Wang, Jie. “Geometry of general curves via degenerations and deformations.” 2010. Doctoral Dissertation, The Ohio State University. Accessed August 14, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1291067498.

MLA Handbook (7th Edition):

Wang, Jie. “Geometry of general curves via degenerations and deformations.” 2010. Web. 14 Aug 2020.

Vancouver:

Wang J. Geometry of general curves via degenerations and deformations. [Internet] [Doctoral dissertation]. The Ohio State University; 2010. [cited 2020 Aug 14]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1291067498.

Council of Science Editors:

Wang J. Geometry of general curves via degenerations and deformations. [Doctoral Dissertation]. The Ohio State University; 2010. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1291067498

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