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Towards refined curve counting on the Enriques surface II: Motivic refinements
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Towards refined curve counting on the Enriques surface II: Motivic refinements
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We study the motivic Pandharipande-Thomas invariants of the Enriques Calabi-Yau threefolds in fiber curve classes by basic computations and analysis of a wallcrossing formula of Toda. Motivated by our results we conjecture a formula for the perverse Hodge numbers of the compactified Jacobian fibration of linar systems on Enriques surfaces in terms of its Betti numbers. This leads to an asymptotic for said Hodge numbers and raises questions about the behaviour of the extremal Hodge numbers.
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Cited by 1 Pith paper
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Stabilization of intersection Betti numbers for moduli spaces of one-dimensional sheaves on surfaces
For Enriques and bielliptic surfaces, the intersection Betti numbers of moduli spaces of one-dimensional semistable sheaves stabilize to Göttsche's stable Betti numbers of Hilbert schemes.
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