On the Hilbert scheme of degeneracy loci of twisted differential forms
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Abstract:
We prove that, for $3 < m < n-1$, the Grassmannian of $m$-dimensional subspaces of the space of skew-symmetric forms over a vector space of dimension $n$ is birational to the Hilbert scheme of degeneracy loci of $m$ global sections of $\Omega _{\mathbb {P}^{n-1}}(2)$, the twisted cotangent bundle on $\mathbb {P}^{n-1}$. For $3=m<n-1$ and $n$ odd, this Grassmannian is proved to be birational to the set of Veronese surfaces parameterized by the Pfaffians of linear skew-symmetric matrices of order $n$.References
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Additional Information
- Fabio Tanturri
- Affiliation: Mathematik und Informatik, Universität des Saarlandes, Campus E2 4, D-66123, Saarbrücken, Germany
- Address at time of publication: Institut de Mathématiques de Marseille, Aix-Marseille Université, Technopôle Château-Gombert, 13453 Marseille, France
- MR Author ID: 1050115
- Email: tanturri@math.uni-sb.de, fabio.tanturri@univ-amu.fr
- Received by editor(s): May 6, 2014
- Published electronically: November 18, 2015
- Additional Notes:
This research was supported by the International School for Advanced Studies (SISSA, Trieste), and partially supported by the Research Network Program “GDRE-GRIFGA”, the ANR project GeoLMI
, and by the PRIN 2010/2011 “Geometria delle varietà algebriche”
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 4561-4583
- MSC (2010): Primary 14C05, 14M12; Secondary 14E05, 14J40, 14N15
- DOI: https://doi.org/10.1090/tran/6637
- MathSciNet review: 3456154