Jumps, folds, and hypercomplex structures

2019/03/05 by Bielawski, Roger, Peternell, Carolin
#53C26 #53C28 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.01842

Abstract

We investigate the geometry of the Kodaira moduli space M of sections of π:Z→ \mathbb P¹, the normal bundle of which is allowed to jump from \mathcal O(1)ⁿ to \mathcal O(1)^n-2m⊕ \mathcal O(2)^m⊕ \mathcal O^m. In particular, we identify the natural assumptions which guarantee that the Obata connection of the hypercomplex part of M extends to a logarithmic connection on M.

Related

• Jumps, folds, and singularities of Kodaira moduli spaces
• Local Structure of Moduli Spaces
• Hypercomplex structures arising from twistor spaces
• The derived moduli stack of logarithmic flat connections
• Feigin-Odesskii brackets associated with Kodaira cycles and positroid varieties