تقرير
Fundamental group of Galois covers of degree $6$ surfaces
| العنوان: | Fundamental group of Galois covers of degree $6$ surfaces |
|---|---|
| المؤلفون: | Amram, Meirav, Gong, Cheng, Sinichkin, Uriel, Tan, Sheng-Li, Xu, Wan-Yuan, Yoshpe, Michael |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Algebraic Topology, Mathematics - Group Theory, 14D05 (Primary) 14D06, 14H30, 14J10, 20F36 (Secondary) |
| الوصف: | In this paper we consider the Galois covers of algebraic surfaces of degree 6, with all associated planar degenerations. We compute the fundamental groups of those Galois covers, using their degeneration. We show that for 8 types of degenerations the fundamental group of the Galois cover is non-trivial and for 20 types it is trivial. Moreover, we compute the Chern numbers of all the surfaces with this type of degeneration and prove that the signatures of all their Galois covers are negative. We formulate a conjecture regarding the structure of the fundamental groups of the Galois covers based on our findings. With an appendix by the authors listing the detailed computations and an appendix by Guo Zhiming classifying degree 6 planar degenerations. Comment: Main paper is 21 pages and contains 7 figures. The appendix is 65 pages and contains 42 figures. arXiv admin note: substantial text overlap with arXiv:1610.09612 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2012.03279 |
| رقم الأكسشن: | edsarx.2012.03279 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |