Is there too much variety in the execution of the variety metric.
- Award ID(s):
- 1727849
- PAR ID:
- 10110445
- Date Published:
- Journal Name:
- ASME 2019 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2018
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Tu, Loring W (Ed.)We aim in this manuscript to describe a specific notion of geomet- ric positivity that manifests in cohomology rings associated to the flag variety G/B and, in some cases, to subvarieties of G/B. We offer an exposition on the the well-known geometric basis of the homology of G/B provided by Schubert varieties, whose dual basis in cohomology has nonnegative structure constants. In recent work [R. Goldin, L. Mihalcea, and R. Singh, Positivity of Peterson Schubert Calculus, arXiv2106.10372] we showed that the equivariant cohomology of Peterson varieties satisfies a positivity phenomenon similar to that for Schubert calculus for G/B. Here we explain how this positivity extends to this particular nilpotent Hessenberg variety, and offer some open questions about the ingredients for extending positivity results to other Hessenberg varieties.more » « less
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