Flag varieties and schubert calculus
In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry). It was a precursor of several more modern theories, for example characteristic classes, and in particular its algorithmic aspects are still of current interest. The phrase "Schubert calculus" is sometimes used to mean the enumerative geometry of linear sub… http://alpha.math.uga.edu/~wag/
Flag varieties and schubert calculus
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WebA Newton–Okounkov polytope of a complete flag variety can be turned into a convex geometric model for Schubert calculus. Namely, we can represent Schubert cycles by linear combinations of faces ... Webag varieties, we use Schubert classes and quantum Schubert calculus. Let Fl(n;r 1;:::;r ˆ) be the ag variety of quotients of Cn. The detailed description of the rst ingredient { a way of writing the anti-canonical class as a sum of ratios of Schubert classes { is in § 4. For the second ingredient, we use a
WebPart 1. Equivariant Schubert calculus 2 1. Flag and Schubert varieties 2 1.1. Atlases on flag manifolds 3 1.2. The Bruhat decomposition of Gr(k; Cn) 4 1.3. First examples of Schubert calculus 6 1.4. The Bruhat decomposition of flag manifolds 7 1.5. Poincare polynomials of flag manifolds 8´ 1.6. Self-duality of the Schubert basis 9 1.7. WebThere will be an initial focus on Schubert calculus of Grassmannians and full flag varieties; this is the study of the ring structure of the cohomology ring of these varieties. There is then a possibility of extending this study to the equivariant/quantum Schubert calculus, or moving in a different direction and investigating Springer theory ...
WebIn particular, I am interested in equivariant K-theory, cohomology, and Chow groups, as well as problems related to flag varieties, Schubert calculus, and some related combinatorics. A complete list of my published research papers and preprints, as well as a more detailed description of my research interests, is available on my research page .
WebA (complete) flag variety is a variety of the form G / B where G is a (complex, say) reductive algebraic group and B is a Borel subgroup of G. The classical flag variety corresponds to …
WebMar 30, 2012 · The Schubert calculus or Schubert enumerative calculus is a formal calculus of symbols representing geometric conditions used to solve problems in enumerative … solarus consultingWebProducts and services. Our innovative products and services for learners, authors and customers are based on world-class research and are relevant, exciting and inspiring. solarus facebookWebThese varieties include the flag variety and related objects such as Schubert varieties, nilpotent orbits and Springer fibres. Here I have worked on problems such as positivity in … solar underwater light showWebIn the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results … sly softwareWebThere will be an initial focus on Schubert calculus of Grassmannians and full flag varieties; this is the study of the ring structure of the cohomology ring of these varieties. … solarus games downloadWebSCHUBERT CALCULUS ON FLAG MANIFOLDS 1.1 Introduction and Preliminaries 1.1.1 Introduction In this project we discuss a new and effective way of doing intersection theory on flag manifolds. Namely we do Schubert calculus on flag manifolds and flag bundles via equivariant cohomology and localization. The basic idea is to locate slysoft virtual isoWebIn mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F.When F is … sly sourcing