Schubert Varieties in the Flag Variety of Hilbert-Samuel Multiplicity Two
Meek, Kevin Richard. (2020-08). Schubert Varieties in the Flag Variety of Hilbert-Samuel Multiplicity Two. Theses and Dissertations Collection, University of Idaho Library Digital Collections. https://www.lib.uidaho.edu/digital/etd/items/meek_idaho_0089e_11925.html
- Title:
- Schubert Varieties in the Flag Variety of Hilbert-Samuel Multiplicity Two
- Author:
- Meek, Kevin Richard
- Date:
- 2020-08
- Keywords:
- Algebra Combinatorics Schubert
- Program:
- Mathematics
- Subject Category:
- Mathematics
- Abstract:
-
Smooth Schubert varieties were rst characterized in terms of pattern avoidance by Lakshmibai and Sandhya. One way of classifying singularities in a variety is the Hilbert-Samuel multiplicity. We characterize the Schubert varieties of flag manifolds which have
Hilbert-Samuel multiplicity two or less at all points using the Rothe diagram. Our condition is relatively simple and visually easy to distinguish given the Rothe diagram of a Schubert variety. We also show that Schubert varieties with multiplicity two or less at all points
cannot be characterized by pattern avoidance.
- Description:
- doctoral, Ph.D., Mathematics -- University of Idaho - College of Graduate Studies, 2020-08
- Major Professor:
- Woo, Alexander
- Committee:
- Abo, Hirotachi; Rajchgot, Jenna; Tohaneanu, Stefan
- Defense Date:
- 2020-08
- Identifier:
- Meek_idaho_0089E_11925
- Type:
- Text
- Format Original:
- Format:
- application/pdf
- Rights:
- In Copyright - Educational Use Permitted. For more information, please contact University of Idaho Library Special Collections and Archives Department at libspec@uidaho.edu.
- Standardized Rights:
- http://rightsstatements.org/vocab/InC-EDU/1.0/