Classical sheaf cohomology rings on Grassmannians

Jirui Guo Virginia Tech Zhentao Lu University of Oxford Eric Sharpe Virginia Tech

Algebraic Geometry arXiv subject: Algebraic Geometry (math.AG) mathscidoc:2205.45013

Journal of Algebra, 486, 246-287, 2017.10
Let the vector bundle E be a deformation of the tangent bundle over the Grassmannian G(k, n). We compute the ring structure of sheaf cohomology valued in exterior powers of E, also known as the polymology. This is the first part of a project studying the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle, a generalization of ordinary quantum cohomology rings of Grassmannians. A companion physics paper [6] describes physical aspects of the theory, including a conjecture for the quantum sheaf cohomology ring, and numerous examples.
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  title={Classical sheaf cohomology rings on Grassmannians},
  author={Jirui Guo, Zhentao Lu, and Eric Sharpe},
  booktitle={Journal of Algebra},
Jirui Guo, Zhentao Lu, and Eric Sharpe. Classical sheaf cohomology rings on Grassmannians. 2017. Vol. 486. In Journal of Algebra. pp.246-287.
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