Orthosymplectic enumerative geometry

Thesis

This thesis studies enumerative invariants counting orthogonal and symplectic objects in linear categories arising from algebraic geometry, as a first step towards generalizing known results and methods in linear enumerative geometry to general non-linear moduli problems.

The main focus of the thesis is the construction of orthosymplectic Donaldson–Thomas invariants and the study of their properties. Examples include invariants counting self-dual representations of self-dual quivers with potential, invariants counting orthosymplectic complexes of coherent sheaves on Calabi–Yau threefolds, a motivic version of Vafa–Witten type invariants counting orthosymplectic Higgs complexes on surfaces, and so on. We prove wallcrossing formulae relating these invariants for different stability conditions, and we carry out explicit computations in some cases.

Authors: Bu, C

• DOI: 10.5287/ora-m8pkrqjp0
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Donaldson–Thomas invariants; principal bundles; enumerative geometry; moduli stacks
• Subjects: Donaldson-Thomas invariants; Geometry, Enumerative