@article{Antón-Sancho2024, 
author = {Álvaro Antón-Sancho},
title = {A construction of Shatz strata in the polystable  G2-bundles moduli space using Hecke curves},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {11},
pages = {6109-6119},
keywords = {principal bundle, moduli space, G2, Shatz stratification, Hecke curve},
url = {https://www.sciopen.com/article/10.3934/era.2024283},
doi = {10.3934/era.2024283},
abstract = {Let  X be a compact Riemann surface of genus  g≥2 and  M(G2) be the moduli space of polystable principal  G2-bundles over  X. The Harder-Narasimhan types of the bundles induced a stratification of the moduli space  M(G2) called Shatz stratification. In this paper, a description of the Shatz strata of the unstable locus of  M(G2) corresponding to certain family of Harder-Narasimhan types (specifically, those of the form  (λ,μ,0,−μ,−λ) with  μ<λ≤0) was given. For this purpose, a family of vector bundles was constructed in which a 3-form and a 2-form were defined so that it was proved that they were strictly polystable principal  G2-bundles. From this, it was proved that, when the genus of  X was  g≥12, these Shatz strata were the disjoint union of a family of  G2-Hecke curves in  M(G2) that will be constructed along the paper. Therefore, the presented results provided an advance in the knowledge of the geometry of  M(G2) through the study of its Shatz strata and presented a methodological innovation, by using Hecke curves for this study.}
}