JonesBF072007.pdf (678.3 kB)
On the Singular Chern Classes of Schubert Varieties Via Small Resolution
thesis
posted on 2007-07-14, 00:00 authored by Benjamin F JonesWe compute the Chern-Schwartz-MacPherson (CSM) class of a Schubert variety in a Grassmannian using a small resolution introduced by Zelevinsky. As a consequence, we show how to compute the Chern-Mather class using a small resolution instead of the Nash blowup. We use these formulas for CSM classes to prove new cases of a positivity conjecture of Aluffi and Mihalcea. Specifically, we show that codimension 1 coefficients in the CSM class of a Schubert cell are strictly positive and give a closed formula for them.
History
Date Created
2007-07-14Date Modified
2018-11-01Defense Date
2007-06-22Research Director(s)
Sam EvensCommittee Members
Sam Evens Matthew Dyer Bruce Williams Michael GekhtmanDegree
- Doctor of Philosophy
Degree Level
- Doctoral Dissertation
Language
- English
Alternate Identifier
etd-07142007-091253Publisher
University of Notre DameProgram Name
- Mathematics
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