PreprintCC BY 4.0arXiv
Counting Irreducible Components of the Semistable Global Nilpotent Cone
Abstract
We discuss various methods for parametrizing and counting irreducible components of the global nilpotent cone of semistable G-Higgs bundles on a smooth complex curve. By restricting our study to the case of generically regular components following previous work of Faergeman and Raskin, we obtain explicit counts of semistable generically regular irreducible components for G = SLn, and give the first examples of such counts outside type A. These numbers are obtained by counting points in some natural polytopes associated to G, but our method requires a finer analysis in cases where the center of the group G is disconnected.
Related
- Socle formulas for rigid irreducible components of Lusztig's nilpotent varieties in type A
- Rank 3 curve semistable Higgs bundles: the nilpotent case
- Counting irreducible skew polynomials x2n+axn+1
- Counting Nilpotent Galois extensions with prescribed genus number
- Irreducible components of crystabelline deformation rings: the wildly ramified case
BibTeX
@misc{seroux2026counting,
title = {{Counting Irreducible Components of the Semistable Global Nilpotent Cone}},
author = {Nicolas Seroux},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26085},
eprint = {2610.26085},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26085},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Counting Irreducible Components of the Semistable Global Nilpotent Cone
AU - Nicolas Seroux
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26085
UR - https://arxiv.org/abs/2610.26085
AB - We discuss various methods for parametrizing and counting irreducible components of the global nilpotent cone of semistable G-Higgs bundles on a smooth complex curve. By restricting our study to the case of generically regular components following previous work of Faergeman and Raskin, we obtain explicit counts of semistable generically regular irreducible components for G = SL_n, and give the first examples of such counts outside type A. These numbers are obtained by counting points in some natural polytopes associated to G, but our method requires a finer analysis in cases where the center of the group G is disconnected.
ER -