PreprintCC BY 4.0arXiv
Universal Formulas for de Jonquières Loci and Equivariant Contact Problems
Abstract
Given a family of genus g curves f:Ψ→ S and a relative degree d line bundle L on Ψ such that f*L is a vector bundle, the projectivization ℙ(f*L) is stratified by relative de Jonquières loci, which parameterize sections of L with prescribed vanishing orders. We give universal formulas for the classes of these loci in terms of the relative O(1) on ℙ(f*L) and tautological classes pulled back from the universal Picard stack Picgd. When f is the family of lines in ℙr, we use the universal polynomials to compute GLr+1-equivariant classes of loci of hypersurfaces and complete intersections admitting lines with prescribed contact orders.
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BibTeX
@misc{rajan2026universal,
title = {{Universal Formulas for de Jonquières Loci and Equivariant Contact Problems}},
author = {Smita Rajan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30892},
eprint = {2609.30892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30892},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universal Formulas for de Jonquières Loci and Equivariant Contact Problems
AU - Smita Rajan
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30892
UR - https://arxiv.org/abs/2609.30892
AB - Given a family of genus g curves f:Ψ→ S and a relative degree d line bundle L on Ψ such that f_*L is a vector bundle, the projectivization ℙ(f_*L) is stratified by relative de Jonquières loci, which parameterize sections of L with prescribed vanishing orders. We give universal formulas for the classes of these loci in terms of the relative O(1) on ℙ(f_*L) and tautological classes pulled back from the universal Picard stack Pic_g^d. When f is the family of lines in ℙ^r, we use the universal polynomials to compute GL_r+1-equivariant classes of loci of hypersurfaces and complete intersections admitting lines with prescribed contact orders.
ER -