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A1-Brouwer Degrees and Applications to Enriched Enumerative Geometry / Thomas Brazelton.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Brazelton, Thomas, author.
- Language:
- English
- Subjects (All):
- Mathematics.
- Theoretical mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Local Subjects:
- Mathematics.
- Theoretical mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Physical Description:
- 1 online resource (206 pages)
- Distribution:
- Ann Arbor : ProQuest Dissertations & Theses, 2023
- Contained In:
- Dissertations Abstracts International 84-12B.
- Place of Publication:
- [Philadelphia, Pennsylvania] : University of Pennsylvania, 2022.
- Language Note:
- English
- Summary:
- A1 -enumerative geometry, or enriched enumerative geometry, is a recent program of mathematics following work of Kass-Wickelgren, Levine and others, which wields tools from motivic homotopy theory in order to investigate enumerative geometry problems over arbitrary fields. One of the key constructions used in this program is an algebrao-geometric analogue of the Brouwer degree, called the A1 -Brouwer degree, first defined by Morel. Early computational results for A 1 -Brouwer degrees include Cazanave's thesis, and work of Kass and Wickelgren comparing A 1 -Brouwer degrees at rational points with the Eisenbud-Khishiashvili-Levine signature formula. However a few years ago, the general question of computing an A 1 -Brouwer degree of an endomorphism of affine space with an isolated zero at an arbitrary closed point was largely open. We report on work which closes this gap, providing a suite of computational tools, and discussing applications to enriched enumerative geometry.
- Notes:
- Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
- Advisors: Merling, Mona; Wickelgren, Kirsten; Committee members: Krashen, Daniel; Gluck, Herman.
- Department: Mathematics.
- Ph.D. University of Pennsylvania 2023.
- Local Notes:
- School code: 0175
- ISBN:
- 9798379755799
- Access Restriction:
- Restricted for use by site license.
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