Motivic Milnor fiber of cyclic L-infinity algebras

Abstract

We define motivic Milnor fiber of cyclic $L_{\infty }$-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topological Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by $L$ is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that Behrend function depends only on the formal neighborhood of the moduli space.

17 pages. Comments are very welcome

References in corpus (7)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Lie theory for nilpotent L-infinity algebras
• Donaldson-Thomas invariants via microlocal geometry
• Desingularization of quasi-excellent schemes in characteristic zero
• Deformation theory via differential graded Lie algebras
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Cited by in corpus (7)

• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• On motivic Joyce-Song formula for the Behrend function identities
• The Thom-Sebastiani theorem for the Euler characteristic of cyclic L-infinity algebras
• The moduli space of stable coherent sheaves via non-archimedean geometry
• Motivic virtual signed Euler characteristics and applications to Vafa-Witten invariants
• Donaldson-Thomas invariants of Calabi-Yau orbifolds under flops
• Note on the motivic DT/PT correspondence and the motivic Flop formula