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Series of Fano quiver moduli from extended Dynkin quivers
Abstract
Associated to small extended Dynkin quivers, we construct series of Fano varieties of fixed Picard rank at most five and arbitrary even dimension, which admit a very explicit description of their geometry. For example, they all admit a flat morphism to a projective space, whose general fiber is a product of projective lines. We also give a closed formula for all Betti numbers, and interpret this formula in terms of an action of a cohomological Hall algebra on the cohomology of all the varieties in a series.
Related
BibTeX
@misc{belmans2026series,
title = {{Series of Fano quiver moduli from extended Dynkin quivers}},
author = {Pieter Belmans and Markus Reineke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22203},
eprint = {2610.22203},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22203},
}
RIS
TY - UNPB
TI - Series of Fano quiver moduli from extended Dynkin quivers
AU - Pieter Belmans
AU - Markus Reineke
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22203
UR - https://arxiv.org/abs/2610.22203
AB - Associated to small extended Dynkin quivers, we construct series of Fano varieties of fixed Picard rank at most five and arbitrary even dimension, which admit a very explicit description of their geometry. For example, they all admit a flat morphism to a projective space, whose general fiber is a product of projective lines. We also give a closed formula for all Betti numbers, and interpret this formula in terms of an action of a cohomological Hall algebra on the cohomology of all the varieties in a series.
ER -