Gröbner bases for (partial) flag manifolds. (November 2020)

• Record Type: Journal Article
• Authors: Petrović, Zoran Z.; Prvulović, Branislav I.; Radovanović, Marko
• Is Part Of: Journal of symbolic computation. Volume 101(2020)
• Page Start: 90
• Page End: 108
• Publication Date: 2020-11
• Subjects: Gröbner bases -- Flag manifolds -- Borel description -- Chern classes; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.06.008
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: For an arbitrary complex (partial) flag manifold F, a Gröbner basis for the ideal which (in the Borel picture) determines the cohomology algebra H ⁎ ( F ; Z ) is obtained. This Gröbner basis is used to derive multiplication rules for a convenient additive basis of H ⁎ ( F ; Z ) given in terms of Chern classes of the canonical bundles over F . The analogous Gröbner bases related to the mod 2 cohomology of real flag manifolds are also presented.