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- W3044890820 abstract "Recently, Marian–Oprea–Pandharipande established (a generalization of) Lehn's conjecture for Segre numbers associated to Hilbert schemes of points on surfaces. Extending the work of Johnson, they provided a conjectural correspondence between Segre and Verlinde numbers. For surfaces with holomorphic 2-form, we propose conjectural generalizations of their results to moduli spaces of stable sheaves of any rank. Using Mochizuki's formula, we derive a universal function which expresses virtual Segre and Verlinde numbers of surfaces with holomorphic 2-form in terms of Seiberg–Witten invariants and intersection numbers on products of Hilbert schemes of points. We prove that certain canonical virtual Segre and Verlinde numbers of general type surfaces are topological invariants and we verify our conjectures in examples. The power series in our conjectures are algebraic functions, for which we find expressions in several cases and which are permuted under certain Galois actions. Our conjectures imply an algebraic analog of the Mariño–Moore conjecture for higher rank Donaldson invariants. For ranks 3 and 4, we obtain explicit expressions for Donaldson invariants in terms of Seiberg–Witten invariants." @default.
- W3044890820 created "2020-07-29" @default.
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- W3044890820 date "2022-06-23" @default.
- W3044890820 modified "2023-10-15" @default.
- W3044890820 title "Virtual Segre and Verlinde numbers of projective surfaces" @default.
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- W3044890820 doi "https://doi.org/10.1112/jlms.12641" @default.
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