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Spaces of conics on low degree complete intersections


Author: Xuanyu Pan
Journal: Trans. Amer. Math. Soc. 370 (2018), 5381-5400
MSC (2010): Primary 14C05, 14C40, 14D06, 14H50, 14N05
DOI: https://doi.org/10.1090/tran/7107
Published electronically: December 27, 2017
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Abstract: Let $ X$ be a smooth complete intersection contained in $ \mathbb{P}^n_{\mathbb{C}}$ and of low degree. We consider conics contained in $ X$ and passing through two general points of $ X$. We show that the moduli space of these conics is a smooth complete intersection in a projective space. The main ingredients of the proof are a criterion for characterizing when a smooth projective variety is a complete intersection in a projective space, the Grothendieck-Riemann-Roch theorem, and the geometry of spaces of conics.


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Additional Information

Xuanyu Pan
Affiliation: Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130
Email: pan@math.wustl.edu

DOI: https://doi.org/10.1090/tran/7107
Received by editor(s): March 31, 2016
Received by editor(s) in revised form: April 8, 2016, May 21, 2016, September 14, 2016, October 7, 2016, and October 22, 2016
Published electronically: December 27, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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