The meromorphic Hitchin fibration over stable pointed curves: moduli spaces

Autor:	Donagi, Ron, Herrero, Andres Fernandez
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry 14D23 14D20 (Primary) 14H10 14H70 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We construct a universal partial compactification of the relative moduli space of semistable meromorphic Higgs bundles over the stack of stable pointed curves. It parametrizes meromorphic Gieseker Higgs bundles, and is equipped with a flat and proper extension of the usual Hitchin morphism. Over an open subset of the Hitchin base parametrizing allowable nodal spectral covers, we describe the relation of the fibers to compactified Jacobians, thus establishing an analogue of the BNR correspondence. We also construct a version of the moduli space where we require the residues of the meromorphic Higgs bundle to lie in a given set of nilpotent conjugacy classes. In this latter case, we show that there is a flat and proper Hitchin morphism to the flat degeneration of the corresponding family of Hitchin bases constructed in previous physics work. Comment: 41 pages. Comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.16912 Zobrazit plný text záznamu View this record from Arxiv