Type
Text
Type
Dissertation
Advisor
Starr, Jason M | Starr, Jason | Grushevsky, Samuel | Lazarsfeld, Robert | Beheshti, Roya.
Date
2014-12-01
Keywords
Mathematics
Department
Department of Mathematics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76409
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
In this thesis we consider the space of rational curves on a smooth cyclic cover of Pn. These varieties are the simplest examples of Fano varieties beyond the classical examples of complete intersections in homogeneous spaces. We show that for a general cyclic cover, the Kontsevich moduli stack of stable curves in X is irreducible and has the expected dimension. Specifically, let X be a general smooth cyclic cover of Pn of degree r branched over a divisor of degree rd, and let M(X,e) be the Kontsevich moduli stack of stable rational curves of degree e on X. We show that if 2d(r-1)
Recommended Citation
Smith, Lloyd, "The Kontsevich Space of Rational Curves on Cyclic Covers of Projective Space" (2014). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2332.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2332