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Transactions of the American Mathematical Society

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

 
 

 

Blowup algebras of rational normal scrolls


Author: Alessio Sammartano
Journal: Trans. Amer. Math. Soc. 373 (2020), 797-818
MSC (2010): Primary 13A30, 13C40; Secondary 05E45, 13D02, 13P10, 14M12, 14J40
DOI: https://doi.org/10.1090/tran/7689
Published electronically: November 5, 2019
MathSciNet review: 4068250
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Abstract | References | Similar Articles | Additional Information

Abstract: We determine the equations of the blowup of $\mathbb {P}^{n}$ along a $d$-fold rational normal scroll $\mathcal {S}$, and we prove that the Rees ring and special fiber ring of $\mathcal {S}\subseteq \mathbb {P}^{n}$ are Koszul algebras.


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Additional Information

Alessio Sammartano
Affiliation: Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, Indiana 46556
MR Author ID: 942872
ORCID: 0000-0002-0377-1375
Email: asammart@nd.edu

Keywords: Rees ring, special fiber, determinantal ideal, variety of minimal degree, Gröbner basis, Koszul algebra, simplicial complex, non-crossing sets, Catalan numbers
Received by editor(s): September 29, 2017
Received by editor(s) in revised form: February 11, 2018, and July 17, 2018
Published electronically: November 5, 2019
Additional Notes: This work was supported by a fellowship of the Purdue Research Foundation while the author was visiting the University of Genoa in 2016 and by grant No. 1440140 of the National Science Foundation while he was a Postdoctoral Fellow at the Mathematical Sciences Research Institute in Berkeley in 2018.
Article copyright: © Copyright 2019 American Mathematical Society