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The Arithmetic of Del Pezzo Surfaces and Hilbert Schemes of Points
The Arithmetic of Del Pezzo Surfaces and Hilbert Schemes of Points
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103145
- ISBN
- 9798314895962
- DDC
- 510
- 저자명
- Porzio, Morena.
- 서명/저자
- The Arithmetic of Del Pezzo Surfaces and Hilbert Schemes of Points
- 발행사항
- [Sl] : Columbia University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 123 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
- 주기사항
- Advisor: de Jong, Aise Johan.
- 학위논문주기
- Thesis (Ph.D.)--Columbia University, 2025.
- 초록/해제
- 요약Motivated by the Cassels-Swinnerton-Dyer Conjecture for cubic surfaces, this thesis investigates the stable birational class of Hilb\uD835\uDC5B\uD835\uDC4B , the Hilbert scheme of length \uD835\uDC5B closed subschemes on a given surface \uD835\uDC4B. The primary focus is to determine for which pairs of positive integers (\uD835\uDC5B, \uD835\uDC5B' ) the varieties Hilb\uD835\uDC5B\uD835\uDC4B and Hilb\uD835\uDC5B '\uD835\uDC4B are stably birational, specifically when \uD835\uDC4B is a surface with irregularity \uD835\uDC5E(\uD835\uDC4B) = 0.After establishing general results for such surfaces, the study narrows its scope to geometrically rational surfaces. In this case, it is shown that, among the Hilb\uD835\uDC5B\uD835\uDC4B 's, there exist only finitely many stable birational classes. A corollary of this finding is the rationality of the motivic zeta function \uD835\uDF01mot(\uD835\uDC4B, \uD835\uDC61) in \uD835\uDC3E0 (Var/\uD835\uDC58)/( [\uD835\uDD38 1 \uD835\uDC58 ]) [ [\uD835\uDC61]] over fields of characteristic zero.Returning to cubic surfaces, the thesis further examines the stable birational types of Hilb\uD835\uDC5B\uD835\uDC4B both asymptotically and for small values of \uD835\uDC5B.
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 기타저자
- Columbia University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-11B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202103145
■006m o d
■007cr#unu||||||||
■020 ▼a9798314895962
■035 ▼a(MiAaPQ)AAI31995331
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aPorzio, Morena.
■24510▼aThe Arithmetic of Del Pezzo Surfaces and Hilbert Schemes of Points
■260 ▼a[Sl]▼bColumbia University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a123 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-11, Section: B.
■500 ▼aAdvisor: de Jong, Aise Johan.
■5021 ▼aThesis (Ph.D.)--Columbia University, 2025.
■520 ▼aMotivated by the Cassels-Swinnerton-Dyer Conjecture for cubic surfaces, this thesis investigates the stable birational class of Hilb\uD835\uDC5B\uD835\uDC4B , the Hilbert scheme of length \uD835\uDC5B closed subschemes on a given surface \uD835\uDC4B. The primary focus is to determine for which pairs of positive integers (\uD835\uDC5B, \uD835\uDC5B' ) the varieties Hilb\uD835\uDC5B\uD835\uDC4B and Hilb\uD835\uDC5B '\uD835\uDC4B are stably birational, specifically when \uD835\uDC4B is a surface with irregularity \uD835\uDC5E(\uD835\uDC4B) = 0.After establishing general results for such surfaces, the study narrows its scope to geometrically rational surfaces. In this case, it is shown that, among the Hilb\uD835\uDC5B\uD835\uDC4B 's, there exist only finitely many stable birational classes. A corollary of this finding is the rationality of the motivic zeta function \uD835\uDF01mot(\uD835\uDC4B, \uD835\uDC61) in \uD835\uDC3E0 (Var/\uD835\uDC58)/( [\uD835\uDD38 1 \uD835\uDC58 ]) [ [\uD835\uDC61]] over fields of characteristic zero.Returning to cubic surfaces, the thesis further examines the stable birational types of Hilb\uD835\uDC5B\uD835\uDC4B both asymptotically and for small values of \uD835\uDC5B.
■590 ▼aSchool code: 0054.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■653 ▼aBirational geometry
■653 ▼aCassels--Swinnerton-Dyer Conjecture
■653 ▼aHilbert schemes of points
■653 ▼aMotivic zeta function
■653 ▼aBirational classes
■690 ▼a0405
■690 ▼a0364
■71020▼aColumbia University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-11B.
■790 ▼a0054
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17357190▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
