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A1-Brouwer Degrees and Applications to Enriched Enumerative Geometry- [electronic resource]
A1-Brouwer Degrees and Applications to Enriched Enumerative Geometry- [electronic resource]
상세정보
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214100123
- ISBN
- 9798379755799
- DDC
- 510
- 서명/저자
- A1-Brouwer Degrees and Applications to Enriched Enumerative Geometry - [electronic resource]
- 발행사항
- [S.l.]: : University of Pennsylvania., 2023
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2023
- 형태사항
- 1 online resource(206 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
- 주기사항
- Advisor: Merling, Mona;Wickelgren, Kirsten.
- 학위논문주기
- Thesis (Ph.D.)--University of Pennsylvania, 2023.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 요약A1 -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.
- 일반주제명
- Mathematics.
- 일반주제명
- Theoretical mathematics.
- 키워드
- Endomorphism
- 키워드
- Brouwer degree
- 기타저자
- University of Pennsylvania Mathematics
- 기본자료저록
- Dissertations Abstracts International. 84-12B.
- 기본자료저록
- Dissertation Abstract International
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
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■020 ▼a9798379755799
■035 ▼a(MiAaPQ)AAI30424779
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aBrazelton, Thomas.
■24510▼aA1-Brouwer Degrees and Applications to Enriched Enumerative Geometry▼h[electronic resource]
■260 ▼a[S.l.]:▼bUniversity of Pennsylvania. ▼c2023
■260 1▼aAnn Arbor :▼bProQuest Dissertations & Theses, ▼c2023
■300 ▼a1 online resource(206 p.)
■500 ▼aSource: Dissertations Abstracts International, Volume: 84-12, Section: B.
■500 ▼aAdvisor: Merling, Mona;Wickelgren, Kirsten.
■5021 ▼aThesis (Ph.D.)--University of Pennsylvania, 2023.
■506 ▼aThis item must not be sold to any third party vendors.
■520 ▼aA1 -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.
■590 ▼aSchool code: 0175.
■650 4▼aMathematics.
■650 4▼aTheoretical mathematics.
■653 ▼aEnumerative geometry
■653 ▼aEndomorphism
■653 ▼aComputational tool
■653 ▼aBrouwer degree
■690 ▼a0405
■690 ▼a0642
■71020▼aUniversity of Pennsylvania▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g84-12B.
■773 ▼tDissertation Abstract International
■790 ▼a0175
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T16931820▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
■980 ▼a202402▼f2024
