3 papers
math.AG2025
A Hopf index for isotropic sections of orthogonal bundles
Martijn Kool, Jeongseok Oh, Jørgen Vold Rennemo +1
The Hopf index equates the multiplicity of a zero of a section of a vector bundle with a winding number. We give eight analogues for isotropic sections of bundles with quadratic fo…
math.AG2024
Refined sheaf counting on local K3 surfaces
Richard P. Thomas
We compute all refined sheaf counting invariants -- Vafa-Witten, reduced DT, stable pairs and Gopakumar-Vafa -- for all classes on local surfaces. Along the way we develop ran…
math.AG2024
Quantum Lefschetz without curves
Jeongseok Oh, Richard P. Thomas
Given one quasi-smooth derived space cut out of another by a section of a 2-term complex of bundles, we give two formulae for its virtual cycle. They are modelled on the the -fi…