Brill-Noether-type theorems with a movable ramification point

• Main Author: Lehman, Rebecca C. (Rebecca Colleen)
• Other Authors: Jason M. Starr.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2007
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/38885

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). === 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. === by Rebecca C. Lehman. === Ph.D.