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
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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.
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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