PreprintCC BY-NC-SA 4.0arXiv
Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings
Abstract
For an n-fold geometrically cyclic branched covering Y of a smooth, projective scheme X branched at a smooth closed subscheme Z⊂ X with n ∈ k×, we compute the quadratic Euler characteristic of Y in terms of certain Euler classes on X and Z using the quadratic Riemann-Hurwitz formula of Levine. When n is odd, we relate the quadratic Euler characteristic of Y to the quadratic Euler characteristics of X and Z, obtaining similar formulae to the situation in topology. As an application, we compute the quadratic Euler characteristic of geometrically cyclic branched double coverings of ℙ2.
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BibTeX
@misc{broring2026quadratic,
title = {{Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings}},
author = {Louisa F. Bröring},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.13425},
eprint = {2605.13425},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.13425},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings
AU - Louisa F. Bröring
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2605.13425
UR - https://arxiv.org/abs/2605.13425
AB - For an n-fold geometrically cyclic branched covering Y of a smooth, projective scheme X branched at a smooth closed subscheme Z⊂ X with n ∈ k^×, we compute the quadratic Euler characteristic of Y in terms of certain Euler classes on X and Z using the quadratic Riemann-Hurwitz formula of Levine. When n is odd, we relate the quadratic Euler characteristic of Y to the quadratic Euler characteristics of X and Z, obtaining similar formulae to the situation in topology. As an application, we compute the quadratic Euler characteristic of geometrically cyclic branched double coverings of ℙ^2.
ER -