تقرير
Holomorphic Higgs bundles over the Teichm\'uller space
| العنوان: | Holomorphic Higgs bundles over the Teichm\'uller space |
|---|---|
| المؤلفون: | Biswas, Indranil, Heller, Lynn, Heller, Sebastian |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, Mathematics - Complex Variables, 53C07, 14D05, 57R56, 32G15 |
| الوصف: | We study which representations $\rho$ of the fundamental group of a compact oriented surface $X$ admit Higgs data that depend holomorphically on the Riemann surface $\Sigma\,=\, (X,\, J)$ via non-abelian Hodge correspondence. For representations $\rho$ into $\mathrm{SL}(2,\mathbb C)$ we show that holomorphic dependency is equivalent to $\rho$ being unitary. For higher ranks this equivalence fails -- we show the existence of non-unitary and irreducible representations of the fundamental group into $\mathrm{SL}(n,\mathbb C)$ admitting Higgs data that are holomorphic in $\Sigma$, for $n$ large enough. Comment: 14 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2308.13860 |
| رقم الأكسشن: | edsarx.2308.13860 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |