S[subscript n]-equivariant sheaves and Koszul cohomology
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s40687-014-0010-9.pdf
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Author(s)
Yang, David H.
Date Issued
November 2014
Journal
Research in the Mathematical Sciences
Publisher
Springer
Citation
Yang, David H. “S n -Equivariant Sheaves and Koszul Cohomology.” Mathematical Sciences 1, no. 1 (December 2014).
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1186/s40687-014-0010-9
