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S[subscript n]-equivariant sheaves and Koszul cohomology

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  • Author(s): Yang, David H.
  • Document Type:
    article in journal/newspaper
  • Language:
    English
  • Additional Information
    • Contributors:
      Massachusetts Institute of Technology. Department of Mathematics; Yang, David H.
    • Publication Information:
      Springer
    • Publication Date:
      2014
    • Collection:
      DSpace@MIT (Massachusetts Institute of Technology)
    • Abstract:
      Purpose: We give a new interpretation of Koszul cohomology, which is equivalent under the Bridgeland-King-Reid equivalence to Voisin's Hilbert scheme interpretation in dimensions 1 and 2 but is different in higher dimensions. Methods: We show that an explicit resolution of a certain S[subscript n]-equivariant sheaf is equivalent to a resolution appearing in the theory of Koszul cohomology. Results: Our methods easily show that the dimension K[subscript p,q](B,L) is a polynomial in d for L=dA+P with A ample and d large enough. Conclusions: This interpretation allows us to extract various pieces of information about asymptotic properties Kp,q for fixed p,q. ; National Science Foundation (U.S.). Research Experience for Undergraduates (Program)
    • File Description:
      application/pdf
    • ISSN:
      2197-9847
    • Relation:
      http://dx.doi.org/10.1186/s40687-014-0010-9; Research in the Mathematical Sciences; http://hdl.handle.net/1721.1/91930; Yang, David H. “S n -Equivariant Sheaves and Koszul Cohomology.” Mathematical Sciences 1, no. 1 (December 2014).
    • Online Access:
      https://doi.org/10.1186/s40687-014-0010-9
      http://hdl.handle.net/1721.1/91930
    • Rights:
      http://creativecommons.org/licenses/by/2.0 ; David H Yang et al.; licensee BioMed Central Ltd.
    • Accession Number:
      edsbas.4EA03E38