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On the Superabundance of Singular Varieties in Positive Characteristic.

Record Type:	Electronic resources : Monograph/item
Title/Author:	On the Superabundance of Singular Varieties in Positive Characteristic./
Author:	Kettinger, Jake.
Description:	1 online resource (73 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30489213click for full text (PQDT)
ISBN:	9798379515713

On the Superabundance of Singular Varieties in Positive Characteristic.
Kettinger, Jake.

On the Superabundance of Singular Varieties in Positive Characteristic. - 1 online resource (73 pages)

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

Thesis (Ph.D.)--The University of Nebraska - Lincoln, 2023.

Includes bibliographical references

The geproci property is a recent development in the world of geometry. We call a set of points Z\\subseq\\P_k.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379515713Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Algebraic geometryIndex Terms--Genre/Form:

542853
Electronic books.

On the Superabundance of Singular Varieties in Positive Characteristic.
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100 1 $a Kettinger, Jake. $3 3698303
245 1 0 $a On the Superabundance of Singular Varieties in Positive Characteristic.
264 0 $c 2023
300 $a 1 online resource (73 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Harbourne, Brian.
502 $a Thesis (Ph.D.)--The University of Nebraska - Lincoln, 2023.
504 $a Includes bibliographical references
520 $a The geproci property is a recent development in the world of geometry. We call a set of points Z\\subseq\\P_k.
520 $a 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 and b. Examples known as grids have been known since 2011. Previously, the study of the geproci property has taken place within the characteristic 0 setting; prior to the work in this thesis, a procedure has been known for creating an (a,b)-geproci half-grid for 4\\leq a\\leq b, but it was not known what other examples there can be. Furthermore, before the work in this thesis, only a few examples of geproci nontrivial non-grid non-half-grids were known and there was no known way to generate more. Here, we use geometry in the positive characteristic setting to give new methods of producing geproci half-grids and non-half-grids. We also pick up work that had been done in 2017 by Solomon Akesseh, who had proven that there are no unexpected cubics in characteristic 3 with distinct points and gave examples involving infinitely near points based on quasi-elliptic fibrations in characteristic 2. Each quasi-elliptic fibration has a Dynkin diagram. Here, in contrast, for each possible Dynkin diagram for a quasi-elliptic fibration in characteristic 3, we give an example of the fibration but show it does not give rise to an unexpected cubic.[Equations Omitted].
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Algebraic geometry
653 $a Combinatorics
653 $a Geproci
653 $a Quasi-elliptic fibrations
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0405
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a The University of Nebraska - Lincoln. $b Mathematics. $3 1030689
773 0 $t Dissertations Abstracts International $g 84-11B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30489213 $z click for full text (PQDT)