PreprintCC BY-NC 4.0HAL
On the size of the fibers of a morphism of algebraic varieties
Abstract
Let u : V → W be a morphism of algebraic varieties. Given an integer m or m = ∞, we prove that the set of y ∈ W such that u -1 (y) has size m, is a constructible set. We also show that this set is locally closed when W is normal and u is finite.
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BibTeX
@misc{mokkadem2026size,
title = {{On the size of the fibers of a morphism of algebraic varieties}},
author = {Abdelkader Mokkadem},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09128},
eprint = {2609.09128},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05743087v2},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - On the size of the fibers of a morphism of algebraic varieties
AU - Abdelkader Mokkadem
PY - 2026
DA - 2026/09/10
PB - HAL
DO - 10.48550/arxiv.2609.09128
UR - https://hal.science/hal-05743087v2
AB - Let u : V → W be a morphism of algebraic varieties. Given an integer m or m = ∞, we prove that the set of y ∈ W such that u -1 (y) has size m, is a constructible set. We also show that this set is locally closed when W is normal and u is finite. .
ER -