Wasserstein Metric Normalization of Projective Cycle Spaces
Abstract
Let X be an irreducible reduced projective subvariety of a Chow variety. On a generic smooth parameter locus, normal motions of resolved components define a quadratic Wasserstein metric, even when the cycles are singular, reducible, or carry multiplicities. Its metric completion is canonically Xν: resolution fibers collapse, whereas distinct normalization branches over the same Chow cycle remain separated. The completed metric admits an exact ambient action formula. For degree-d hypersurfaces, the inner Wq geometry is compact and induces the projective topology for every 1≤ q≤2. For d≥2, the uniform Hölder exponent 1/d is attained and sharp for each such q; when d=1, the comparison is Lipschitz. Elliptic quartics furnish an explicit model of the boundary branching.
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BibTeX
@misc{yang2026wasserstein,
title = {{Wasserstein Metric Normalization of Projective Cycle Spaces}},
author = {Jiaping Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15965},
eprint = {2609.15965},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15965},
}
RIS
TY - UNPB
TI - Wasserstein Metric Normalization of Projective Cycle Spaces
AU - Jiaping Yang
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.15965
UR - https://arxiv.org/abs/2609.15965
AB - Let X be an irreducible reduced projective subvariety of a Chow variety. On a generic smooth parameter locus, normal motions of resolved components define a quadratic Wasserstein metric, even when the cycles are singular, reducible, or carry multiplicities. Its metric completion is canonically X^ν: resolution fibers collapse, whereas distinct normalization branches over the same Chow cycle remain separated. The completed metric admits an exact ambient action formula. For degree-d hypersurfaces, the inner W_q geometry is compact and induces the projective topology for every 1≤ q≤2. For d≥2, the uniform Hölder exponent 1/d is attained and sharp for each such q; when d=1, the comparison is Lipschitz. Elliptic quartics furnish an explicit model of the boundary branching.
ER -