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Type of Document	Dissertation
Author	Jones, Benjamin F
URN	etd-07142007-091253
Title	ON THE SINGULAR CHERN CLASSES OF SCHUBERT VARIETIES VIA SMALL RESOLUTION
Degree	Doctor of Philosophy
Department	Mathematics
Advisory Committee	Advisor Name Title Bruce Williams Committee Member Matthew Dyer Committee Member Michael Gekhtman Committee Member Sam Evens Committee Member
Keywords	singularities Schubert Varieties Chern class MacPherson Chern Class Mather Chern class resolution algebraic group
Date of Defense	2007-06-22
Availability	unrestricted
Abstract We 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.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    JonesBF072007.pdf 694.58 Kb 00:03:12 00:01:39 00:01:26 00:00:43 00:00:03