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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The geproci property in positive characteristic
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by Jake Kettinger;
Proc. Amer. Math. Soc. 152 (2024), 3229-3242
DOI: https://doi.org/10.1090/proc/16809
Published electronically: June 5, 2024

Abstract:

The geproci property is a recent development in the world of geometry. We call a set of points $Z\subseteq \mathbb {P}_k^3$ an $(a,b)$-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point $P$ to a plane is a complete intersection of curves of degrees $a\leq b$. Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were first described in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids.

In this paper, based partly on the author’s thesis, we use a feature of geometry in positive characteristic to give new methods of producing geproci half grids and non-half grids.

References
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Bibliographic Information
  • Jake Kettinger
  • Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
  • MR Author ID: 1442202
  • Email: jkett@colostate.edu
  • Received by editor(s): August 25, 2023
  • Received by editor(s) in revised form: January 24, 2024, and February 5, 2024
  • Published electronically: June 5, 2024
  • Communicated by: Rachel Pries
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3229-3242
  • MSC (2020): Primary 14N20, 14G15, 14G17, 11T06; Secondary 13M10, 14N05, 14N10
  • DOI: https://doi.org/10.1090/proc/16809
  • MathSciNet review: 4767258