The tautological classes of the moduli spaces of stable maps to flag varieties

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2005

Author dc:creator

• Oprea, Dragos Nicolae

Advisor dc:contributor.advisor

• Gang Tian.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/31164

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/31164