English

Strict Bott-Samelson Resolutions of Schubert Varieties

Algebraic Geometry 2018-01-04 v2

Abstract

We explore the relationship between two desingularization techniques for Schubert varieties. The Bott-Samelson resolution is the more common of the two, but it fails to encompass many properties that Hironaka resolutions provide, in particular, being an isomorphism over the smooth locus. Using a computer search, a list of cases where Bott-Samelson resolutions having this "strictness" property is compiled for the n=5,6n=5,6 cases. A conjecture based on these results is formulated and is subsequently verified for n=7,8n=7,8. A comparison between Bott-Samelson resolutions and blow-ups is also provided.

Cite

@article{arxiv.1702.03468,
  title  = {Strict Bott-Samelson Resolutions of Schubert Varieties},
  author = {Sergio Da Silva},
  journal= {arXiv preprint arXiv:1702.03468},
  year   = {2018}
}

Comments

18 pages; Sage code included in ancillary file; Accepted for publication in Experimental Mathematics; Revised version includes new content relating this work to known research. It also includes updated computer results

R2 v1 2026-06-22T18:15:47.266Z