Affordable Access

Access to the full text

Degeneracy loci of twisted differential forms and linear line complexes

Authors
  • Tanturri, Fabio1
  • 1 Universität des Saarlandes, Mathematik und Informatik, Gebäude E.2.4, Saarbrücken, 66123, Germany , Saarbrücken (Germany)
Type
Published Article
Journal
Archiv der Mathematik
Publisher
Springer Basel
Publication Date
Jul 12, 2015
Volume
105
Issue
2
Pages
109–118
Identifiers
DOI: 10.1007/s00013-015-0768-z
Source
Springer Nature
Keywords
License
Yellow

Abstract

We prove that the Hilbert scheme of degeneracy loci of pairs of global sections of ΩPn-1(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega_{\mathbb{P}^{n-1}}^{}(2)}$$\end{document}, the twisted cotangent bundle on Pn-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P}^{n-1}}$$\end{document}, is unirational and dominated by the Grassmannian of lines in the projective space of skew-symmetric forms over a vector space of dimension n. We provide a constructive method to find the fibers of the dominant map. In classical terminology, this amounts to giving a method to realize all the pencils of linear line complexes having a prescribed set of centers. In particular, we show that the previous map is birational when n = 4.

Report this publication

Statistics

Seen <100 times