Degeneration of Sheaves on Fibered Surfaces

Journal article

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.

Authors: Kuhn, N

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Moduli
• Volume: 2
• Article number: e21
• Publication date: 2025-12-31
• Acceptance date: 2025-08-01
• DOI: 10.1112/mod.2025.10011
• EISSN: 2977-1382
• ISSN: 2949-7647
• Language: English
• Keywords: 14D06; 14D20; Donaldson invariants; 14D21; degenerations; 14N35; moduli of sheaves