Brill-Noether-type theorems with a movable ramification point

Author(s)
Lehman, Rebecca C. (Rebecca Colleen)
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Jason M. Starr.
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Abstract
The classical Brill-Noether theorems count the dimension of the family of maps from a general curve of genus g to non-degenerate curves of degree d in projective space Pr. These theorems can be extended to include ramification conditions at fixed general points. This thesis deals with the problem of imposing a ramification condition at an unspecified point. We solve the problem completely in dimension 1, prove a closed-form existence criterion and a finiteness result in dimension 2, and provide an existence test and bound the dimension of the family in the general case.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
 
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
 
Includes bibliographical references (p. 79-81).
 
Date issued
2007
URI
http://hdl.handle.net/1721.1/38885
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.
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