S[subscript n]-equivariant sheaves and Koszul cohomology
Author(s)Yang, David H.
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Research in the Mathematical Sciences
Yang, David H. “S n -Equivariant Sheaves and Koszul Cohomology.” Mathematical Sciences 1, no. 1 (December 2014).
Final published version