The motivic Donaldson-Thomas invariants of (-2) curves

Abstract

In this paper we calculate the motivic Donaldson-Thomas invariants for (-2)-curves arising from 3-fold flopping contractions in the minimal model programme. We translate this geometric situation into the machinery developed by Kontsevich and Soibelman, and using the results and framework developed previously by the authors we describe the monodromy on these invariants. In particular, in contrast to all existing known Donaldson-Thomas invariants for small resolutions of Gorenstein singularities these monodromy actions are nontrivial.

30 pages, 3 figures

References in corpus (7)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Calabi-Yau algebras
• Non-commutative Donaldson-Thomas theory and the conifold
• The Grothendieck group of algebraic stacks
• Proofs of the integral identity conjecture over algebraically closed fields
• Motivic DT-invariants for the one loop quiver with potential
• Motivic Donaldson-Thomas invariants of toric small crepant resolutions

Cited by in corpus (11)

• Donaldson-Thomas theory for categories of homological dimension one with potential
• The local motivic DT/PT correspondence
• The critical CoHA of a quiver with potential
• A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory
• Donaldson-Thomas invariants vs. intersection cohomology for categories of homological dimension one
• Refined invariants of finite-dimensional Jacobi algebras
• Deformed dimensional reduction
• Stability over cDV singularities and other complete local rings
• Donaldson-Thomas invariants of length 2 flops
• An introduction into (motivic) Donaldson-Thomas theory
• Motivic virtual signed Euler characteristics and applications to Vafa-Witten invariants