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arXiv · 2305.19984

Degenerations of Sheaves on Fibered Surfaces

Nikolas Kuhn
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Abstract

We construct moduli stacks of stable sheaves for surfaces fibered over marked nodal curves by using expanded degenerations. These moduli stacks carry a virtual class and therefore give rise to enumerative invariants. In the case of a surface with two irreducible components glued along a smooth divisor, we prove a degeneration formula that relates the moduli space associated to the surface with the relative spaces associated to the two components. For a smooth surface and no markings, our notion of stability agrees with slope stability with respect to a suitable choice of polarization. We apply our results to compute elliptic genera of moduli spaces of stable sheaves on some elliptic surfaces.

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Nikolas Kuhn. 2023-05-31. Degenerations of Sheaves on Fibered Surfaces. https://arxiv.org/abs/2305.19984

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