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On the Singular Chern Classes of Schubert Varieties Via Small Resolution

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posted on 2007-07-14, 00:00 authored by Benjamin F Jones
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.

History

Date Created

2007-07-14

Date Modified

2018-11-01

Defense Date

2007-06-22

Research Director(s)

Sam Evens

Committee Members

Sam Evens Matthew Dyer Bruce Williams Michael Gekhtman

Degree

  • Doctor of Philosophy

Degree Level

  • Doctoral Dissertation

Language

  • English

Alternate Identifier

etd-07142007-091253

Publisher

University of Notre Dame

Program Name

  • Mathematics

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