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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Hilbert scheme of twisted cubics as a simple wall-crossing


Author: Bingyu Xia
Journal: Trans. Amer. Math. Soc. 370 (2018), 5535-5559
MSC (2010): Primary 14F05; Secondary 14H45, 14J60, 18E30
DOI: https://doi.org/10.1090/tran/7150
Published electronically: April 4, 2018
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Abstract: We study the Hilbert scheme of twisted cubics in three-dimensional projective space by using Bridgeland stability conditions. We use wall-crossing techniques to describe its geometric structure and singularities, which reproves the classical result of Piene and Schlessinger.


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Additional Information

Bingyu Xia
Affiliation: Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, Ohio 43210-1174
Email: xia.128@osu.edu

DOI: https://doi.org/10.1090/tran/7150
Keywords: Bridgeland stability conditions, derived categories, moduli spaces, twisted cubics
Received by editor(s): August 29, 2016
Received by editor(s) in revised form: December 3, 2016
Published electronically: April 4, 2018
Additional Notes: This research was partially supported by NSF grants DMS-1302730 and DMS-1523496 (PI Emanuele Macrì) and a Graduate Special Assignment of the Mathematics Department of Ohio State University.
Article copyright: © Copyright 2018 American Mathematical Society

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