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On the Hilbert scheme of degeneracy loci of twisted differential forms

Author: Fabio Tanturri
Journal: Trans. Amer. Math. Soc. 368 (2016), 4561-4583
MSC (2010): Primary 14C05, 14M12; Secondary 14E05, 14J40, 14N15
Published electronically: November 18, 2015
MathSciNet review: 3456154
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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$.

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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

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”
Article copyright: © Copyright 2015 American Mathematical Society

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