The tautological classes of the moduli spaces of stable maps to flag varieties
Name
61214689-MIT.pdf
Description
Full printable version
Size
7.36 MB
Format
Adobe PDF
Checksum (MD5)
93ab06db7899f833d789ebfef7f9fc15
Author(s)
Oprea, Dragos Nicolae
Advisor(s)
Gang Tian.
Date Issued
2005
Publisher
Massachusetts Institute of Technology
Abstract
We study the tautological classes of the Kontsevich-Manin moduli spaces of genus 0 stable maps to SL flag varieties. We prove that the rational cohomology and rational Chow rings of these spaces are isomorphic and that they are generated by tautological classes. In the case when the target is a projective space, we present a second proof of this result in the spirit of Gromov-Witten theory by making use of a suitable torus action. In addition, we explicitly describe a Bialynicki-Birula stratification of the Kontsevich-Manin spaces in terms of the Gathmann-Li spaces of relative stable morphisms. Finally, we analyze the small codimension classes on the space of maps to arbitrary flag varieties. We obtain an explicit description of the Picard groups. We formulate a conjecture about relations between the tautological generators, which we check in low codimension.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 113-116).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
Persistent DSpace Link
