Oriented Schubert calculus in Chow-Witt rings of Grassmannians

  title={Oriented Schubert calculus in Chow-Witt rings of Grassmannians},
  author={M. Wendt},
  journal={arXiv: Algebraic Geometry},
  • M. Wendt
  • Published 2018
  • Mathematics
  • arXiv: Algebraic Geometry
  • We apply the previous calculations of Chow-Witt rings of Grassmannians to develop an oriented analogue of the classical Schubert calculus. As a result, we get complete diagrammatic descriptions of the ring structure in Chow-Witt rings and twisted Witt groups. In the resulting arithmetic refinements of Schubert calculus, the multiplicity of a solution subspace is a quadratic form encoding additional orientation information. We also discuss a couple of applications, such as a Chow-Witt version of… CONTINUE READING

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