Intersection cohomology of pure sheaf spaces using Kirwan's desingularization

초록

Let M-n be the Simpson compactification of twisted ideal sheaves I-L,I-Q(1) where Q is a rank 4 quadratic hypersurface in P-n and L is a linear subspace of dimension n - 2. This paper calculates the intersection Poincare polynomial of M-n using Kirwan's desingularization method. We obtain the intersection Poincare polynomial of the moduli space for one-dimensional sheaves on del Pezzo surfaces of degree >= 8 by considering wall-crossings of stable pairs and complexes. (C) 2020 Elsevier B.V. All rights reserved.

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