2022
Corrêa, Maurício; Jardim, Marcos; Muniz, Alan
Moduli of distributions via singular schemes Journal Article
Em: Mathematische Zeitschrift volume, vol. 301, pp. 2709–2731, 2022.
Resumo | Links | BibTeX | Tags: Hilbert scheme, Syzygy
@article{nokey,
title = {Moduli of distributions via singular schemes},
author = {Maur\'{i}cio Corr\^{e}a and Marcos Jardim and Alan Muniz },
url = {https://link.springer.com/article/10.1007/s00209-022-03001-y},
doi = {https://doi.org/10.1007/s00209-022-03001-y},
year = {2022},
date = {2022-03-05},
journal = {Mathematische Zeitschrift volume},
volume = {301},
pages = {2709\textendash2731},
abstract = {Let X be a smooth projective variety. We show that the map that sends a codimension one distribution on X to its singular scheme is a morphism from the moduli space of distributions into a Hilbert scheme. We describe its fibers and, when X=Pn, compute them via syzygies. As an application, we describe the moduli spaces of degree 1 distributions on P3. We also give the minimal graded free resolution for the ideal of the singular scheme of a generic distribution on P3.},
keywords = {Hilbert scheme, Syzygy},
pubstate = {published},
tppubtype = {article}
}
Let X be a smooth projective variety. We show that the map that sends a codimension one distribution on X to its singular scheme is a morphism from the moduli space of distributions into a Hilbert scheme. We describe its fibers and, when X=Pn, compute them via syzygies. As an application, we describe the moduli spaces of degree 1 distributions on P3. We also give the minimal graded free resolution for the ideal of the singular scheme of a generic distribution on P3.