Foliated and Mather-Jacobian discrepancies via tangential arcs
Abstract
We express the log discrepancies of co-rank one foliations on normal varieties in terms of arc codimensions and differential orders. On smooth threefolds, if a foliation has simple singularities and its separatrices form an algebraic simple normal crossings divisor, we identify its foliated discrepancies with those of an ordinary pair for every divisor centred on the separatrices. This gives adjunction and log canonical threshold formulae. For algebraic images of the separatrices, we estimate changes in boundary orders caused by failure of ideal generation and by descent through the conductor. For locally complete intersection images, comparison on a common resolution yields criteria for equality of discrepancies and bounds on log canonical thresholds.
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BibTeX
@misc{correa2026foliated,
title = {{Foliated and Mather-Jacobian discrepancies via tangential arcs}},
author = {Maurício Corrêa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.01809},
eprint = {2607.01809},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.01809},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Foliated and Mather-Jacobian discrepancies via tangential arcs
AU - Maurício Corrêa
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2607.01809
UR - https://arxiv.org/abs/2607.01809
AB - We express the log discrepancies of co-rank one foliations on normal varieties in terms of arc codimensions and differential orders. On smooth threefolds, if a foliation has simple singularities and its separatrices form an algebraic simple normal crossings divisor, we identify its foliated discrepancies with those of an ordinary pair for every divisor centred on the separatrices. This gives adjunction and log canonical threshold formulae. For algebraic images of the separatrices, we estimate changes in boundary orders caused by failure of ideal generation and by descent through the conductor. For locally complete intersection images, comparison on a common resolution yields criteria for equality of discrepancies and bounds on log canonical thresholds.
ER -