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Products of ideals of linear forms in quadric hypersurfaces


Authors: Aldo Conca, Hop D. Nguyen and Thanh Vu
Journal: Proc. Amer. Math. Soc. 147 (2019), 1867-1880
MSC (2010): Primary 13D02, 13D05
DOI: https://doi.org/10.1090/proc/14393
Published electronically: January 18, 2019
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Abstract: Conca and Herzog proved that any product of ideals of linear forms in a polynomial ring has a linear resolution. The goal of this paper is to establish the same result for any quadric hypersurface. The main tool we develop and use is a flexible version of Derksen and Sidman's approximation systems.


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Additional Information

Aldo Conca
Affiliation: Dipartimento di Matematica, Università Degli Studi di Genova, Via Dodecaneso 35, 16146 Genova, Italy
Email: conca@dima.unige.it

Hop D. Nguyen
Affiliation: Dipartimento di Matematica, Università Degli Studi di Genova, Via Dodecaneso 35, 16146 Genova, Italy
Address at time of publication: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
Email: ngdhop@gmail.com

Thanh Vu
Affiliation: Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam
Email: vuqthanh@gmail.com

DOI: https://doi.org/10.1090/proc/14393
Keywords: Linear resolution, regularity, Koszul algebra, universally Koszul algebra.
Received by editor(s): November 22, 2017
Received by editor(s) in revised form: June 2, 2018
Published electronically: January 18, 2019
Additional Notes: The first author was supported by the Istituto Nazionale di Alta Matematica (INdAM)
The second author is a Marie Curie fellow of INdAM
The third author was partially supported by the Vietnam National Foundation for Science and Technology Development under grant number 101.04-2016.21.
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2019 American Mathematical Society