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Hodge Theoretic Singularities and Hodge Theoretic Aspects of Toric Varieties
Hodge Theoretic Singularities and Hodge Theoretic Aspects of Toric Varieties
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105232
- ISBN
- 9798291567364
- DDC
- 510
- 서명/저자
- Hodge Theoretic Singularities and Hodge Theoretic Aspects of Toric Varieties
- 발행사항
- [Sl] : University of Michigan, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 127 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-03, Section: A.
- 주기사항
- Advisor: Mustata, Mircea.
- 학위논문주기
- Thesis (Ph.D.)--University of Michigan, 2025.
- 초록/해제
- 요약Du Bois and rational singularities are two classes of singularities that show up in some of the most fundamental topics in algebraic geometry, such as the Minimal Model Program, and moduli theory. Over the last few years, there has been a lot of interest in their natural higher analogues, called k-Du Bois and k-rational singularities. These singularities have been extensively studied in the case of local complete intersection (lci) varieties but not much is known outside the lci case. In this thesis, we prove some of the first results in this field beyond the lci setting, with the main theorem being a higher analogue of a classical result of Kovacs, i.e. we prove that the class of varieties with k-Du Bois singularities contains the class of varieties with k-rational singularities, which extends prior results of Mustata-Popa and Friedman-Laza in the lci setting.The second part of the thesis concerns toric varieties, which are a well studied class of algebraic varieties admitting alternate descriptions in terms of convex geometric objects. This thesis proves new local vanishing results on toric varieties and builds on the techniques therein to give a precise formula relating the graded de Rham complex of the intersection cohomology Hodge module of X to the stalks of the intersection cohomology perverse sheaf, when X is a toric variety.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Mathematics education
- 키워드
- Singularities
- 키워드
- Hodge theory
- 키워드
- Toric varieties
- 기타저자
- University of Michigan Mathematics
- 기본자료저록
- Dissertations Abstracts International. 87-03A.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798291567364
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■035 ▼a(MiAaPQ)umichrackham006481
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aVenkatesh, Sridhar.
■24510▼aHodge Theoretic Singularities and Hodge Theoretic Aspects of Toric Varieties
■260 ▼a[Sl]▼bUniversity of Michigan▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a127 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-03, Section: A.
■500 ▼aAdvisor: Mustata, Mircea.
■5021 ▼aThesis (Ph.D.)--University of Michigan, 2025.
■520 ▼aDu Bois and rational singularities are two classes of singularities that show up in some of the most fundamental topics in algebraic geometry, such as the Minimal Model Program, and moduli theory. Over the last few years, there has been a lot of interest in their natural higher analogues, called k-Du Bois and k-rational singularities. These singularities have been extensively studied in the case of local complete intersection (lci) varieties but not much is known outside the lci case. In this thesis, we prove some of the first results in this field beyond the lci setting, with the main theorem being a higher analogue of a classical result of Kovacs, i.e. we prove that the class of varieties with k-Du Bois singularities contains the class of varieties with k-rational singularities, which extends prior results of Mustata-Popa and Friedman-Laza in the lci setting.The second part of the thesis concerns toric varieties, which are a well studied class of algebraic varieties admitting alternate descriptions in terms of convex geometric objects. This thesis proves new local vanishing results on toric varieties and builds on the techniques therein to give a precise formula relating the graded de Rham complex of the intersection cohomology Hodge module of X to the stalks of the intersection cohomology perverse sheaf, when X is a toric variety.
■590 ▼aSchool code: 0127.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■650 4▼aMathematics education
■653 ▼aAlgebraic geometry
■653 ▼aSingularities
■653 ▼aHodge theory
■653 ▼aToric varieties
■690 ▼a0405
■690 ▼a0642
■690 ▼a0280
■71020▼aUniversity of Michigan▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g87-03A.
■790 ▼a0127
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359892▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
