2020/06/17 by Alexandrov, Sergei · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2006.10074
We derive explicit expressions for the generating functions of refined Vafa-Witten invariants Ω(γ,y) of ℙ2 of arbitrary rank N and for their non-holomorphic modular completions. In the course of derivation we also provide: i) a generalization of the recently found generating functions of Ω(γ,y) and their completions for Hirzebruch and del Pezzo surfaces in the canonical chamber of the moduli space to a generic chamber; ii) a version of the blow-up formula expressed directly in terms of these generating functions and its reformulation in a manifestly modular form.