DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Park, Jin-Hyun | - |
dc.contributor.advisor | 박진현 | - |
dc.contributor.author | Bae, Da-Sul | - |
dc.contributor.author | 배다슬 | - |
dc.date.accessioned | 2015-04-29 | - |
dc.date.available | 2015-04-29 | - |
dc.date.issued | 2014 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=569116&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/198127 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수리과학과, 2014.2, [ ii, 43 p. ] | - |
dc.description.abstract | In this paper, we study compact Riemann surfaces, namely a compact connected complex manifold of dimension 1. We first introduce the notion of line bundles and divisors on compact Riemann surfaces, and observe connections with sheaf cohomologies. Next, we prove the Riemann-Roch theorem which plays a significant role in complex analysis and algebraic geometry. We then examine some important applications and consequences of the Riemann-Roch theorem such as Riemann-Hurwitz formula or Clifford`s theorem. In the last few chapters, we introduce the Jacobian of a compact Riemann surface and the Abel-Jacobi map which connects a compact Riemann surface and its Jacobian. We examine some properties of the Abel-Jacobi map and related topic; the theta divisor. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Riemann-Roch theorem | - |
dc.subject | Abel 정리 | - |
dc.subject | Clifford 정리 | - |
dc.subject | Riemann-Hurwitz 공식 | - |
dc.subject | Riemann-Roch 정리 | - |
dc.subject | Abel`s theorem | - |
dc.subject | Riemann-Hurwitz formula | - |
dc.subject | Clifford`s theorem | - |
dc.title | Compact riemann surfaces | - |
dc.title.alternative | 옹골리만면 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 569116/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020123314 | - |
dc.contributor.localauthor | Park, Jin-Hyun | - |
dc.contributor.localauthor | 박진현 | - |
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