On the Singular Chern Classes of Schubert Varieties Via Small Resolution

Doctoral Dissertation

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.

Attributes

Attribute NameValues
URN
  • etd-07142007-091253

Author Benjamin F Jones
Advisor Sam Evens
Contributor Sam Evens, Committee Member
Contributor Matthew Dyer, Committee Member
Contributor Bruce Williams, Committee Member
Contributor Michael Gekhtman, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2007-06-22

Submission Date 2007-07-14
Country
  • United States of America

Subject
  • Mather Chern class

  • MacPherson Chern Class

  • Chern class

  • Schubert Varieties

  • singularities

  • resolution

  • algebraic group

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units

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