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On Arithmetic of Genus 4 Curves
On Arithmetic of Genus 4 Curves
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202104844
- ISBN
- 9798297601024
- DDC
- 510
- 저자명
- Gao, Jiahui.
- 서명/저자
- On Arithmetic of Genus 4 Curves
- 발행사항
- [Sl] : Princeton University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 159 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-04, Section: B.
- 주기사항
- Advisor: Zhang, Shou-Wu.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2025.
- 초록/해제
- 요약We propose and study a new arithmetic invariant of non-hyperelliptic genus-4 curves: a canonical "quadratic" point on the Jacobian, defined by the two natural degree-2 maps to projective lines. Building on Xue's result, that this point is generically non-torsion, we introduce a height-theoretic notion of bigness for families of curves in the moduli space of genus four curves, and give a criterion, via dimensions of modular quotients, for when it holds. We then exhibit two concrete 3- and 4-parameter families (the bi-involutions locus and a CM example) in which the canonical point is provably big, from which we deduce the finiteness of low-height curves and non-torsion at transcendental moduli. Our methods combine adelic Arakelov intersection theory with a generic Betti-rank argument.
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 일반주제명
- Computational physics
- 키워드
- Number theory
- 기타저자
- Princeton University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 87-04B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798297601024
■035 ▼a(MiAaPQ)AAI32173326
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aGao, Jiahui.
■24510▼aOn Arithmetic of Genus 4 Curves
■260 ▼a[Sl]▼bPrinceton University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a159 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-04, Section: B.
■500 ▼aAdvisor: Zhang, Shou-Wu.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2025.
■520 ▼aWe propose and study a new arithmetic invariant of non-hyperelliptic genus-4 curves: a canonical "quadratic" point on the Jacobian, defined by the two natural degree-2 maps to projective lines. Building on Xue's result, that this point is generically non-torsion, we introduce a height-theoretic notion of bigness for families of curves in the moduli space of genus four curves, and give a criterion, via dimensions of modular quotients, for when it holds. We then exhibit two concrete 3- and 4-parameter families (the bi-involutions locus and a CM example) in which the canonical point is provably big, from which we deduce the finiteness of low-height curves and non-torsion at transcendental moduli. Our methods combine adelic Arakelov intersection theory with a generic Betti-rank argument.
■590 ▼aSchool code: 0181.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■650 4▼aComputational physics
■653 ▼aAlgebraic geometry
■653 ▼aArakelov geometry
■653 ▼aArithmetic geometry
■653 ▼aNumber theory
■690 ▼a0405
■690 ▼a0216
■690 ▼a0364
■71020▼aPrinceton University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g87-04B.
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359164▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
