Framed Sheaves over Treefolds and Symmetric Obstruction Theories

We note that open moduli spaces of sheaves over local Calabi-Yau surface geometries framed along the divisor at infinity admit symmetric perfect obstruction theories. We calculate the corresponding Donaldson-Thomas weighted Euler characteristics (as well as the topological Euler characteristics). Furthermore, for blowup geometries, we discuss the contribution of exceptional curves.

2010 Mathematics Subject Classification: 14N35, 14D20

Keywords and Phrases: Moduli spaces of sheaves, Donaldson-Thomas invariants

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