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On Kähler-Einstein fake weighted projective spaces
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 황동선 | - |
| dc.contributor.author | 윤영한 | - |
| dc.date.accessioned | 2022-11-29T02:32:30Z | - |
| dc.date.available | 2022-11-29T02:32:30Z | - |
| dc.date.issued | 2021-02 | - |
| dc.identifier.other | 30867 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/20049 | - |
| dc.description | 학위논문(석사)--아주대학교 일반대학원 :수학과,2021. 2 | - |
| dc.description.abstract | 우리는 fake weighted projective spaces, 즉 Picard number가 1인 Q-factorial projective toric varieties에 대해 연구한다. 첫째, 우리는 Kähler-Einstein 거리 공간이 될 수 있기 위한 fake weighted projective space의 필요충분조건을 찾는다. 둘째, 위의 조건을 사용하여 모든 Kähler-Einstein fake weighted projective space는 B-변환에 대해서 Kähler-Einstein fake weighted projective space가 되고, 모든 3차원 symmetric fake weighted projective space는 Kähler-Einstein 거리 공간이 된다는 것을 보여준다. 또한, 우리는 그 반대가 각각의 경우에 성립되지 않는다는 것을 증명하는 예를 제시한다. 또한 우리는 모든 4보다 크거나 같은 자연수 n에 대해 Kähler-Einstein이 아닌 n차원 symmetric fake weighted projective space의 예를 제시한다. | - |
| dc.description.tableofcontents | 제1장 Introduction 1 제2장 Preliminaries 3 제1절 Notation 3 제2절 Toric Fano varieties 5 제3절 Weighted projective spaces 7 제4절 Fake weighted projective spaces 8 제3장 Fake weighted projective spaces 9 제1절 Existence of a Kähler-Einstein metric 9 제2절 Symmetric fake weighted projective spaces 11 제3절 Barycentric transformations 14 제4장 Remarks on K ̈ahler-Einstein Fano polytopes 15 참고문헌 19 | - |
| dc.language.iso | eng | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | On Kähler-Einstein fake weighted projective spaces | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.department | 일반대학원 수학과 | - |
| dc.date.awarded | 2021. 2 | - |
| dc.description.degree | Master | - |
| dc.identifier.localId | 1203277 | - |
| dc.identifier.uci | I804:41038-000000030867 | - |
| dc.identifier.url | http://dcoll.ajou.ac.kr:9080/dcollection/common/orgView/000000030867 | - |
| dc.subject.keyword | Kähler-Einstein | - |
| dc.subject.keyword | barycentric transformation | - |
| dc.subject.keyword | fake weighted projective space | - |
| dc.subject.keyword | symmetric | - |
| dc.description.alternativeAbstract | We study fake weighted projective spaces, i.e., Q-factorial projective toric varieties of Picard number one. First, we find a necessary and sufficient condition for fake weighted projective spaces to admit a Kähler-Einstein metric. Second, using the above condition, we show that every Kähler-Einstein fake weighted projective space is of type B∞ and every symmetric fake weighted projective 3-space admits a Kähler-Einstein metric. Moreover, we provide examples demonstrating that the converse does not hold in each case. We also give an example of a symmetric fake weighted projective n-space that is not Kähler-Einstein for all n ≥ 4. | - |
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- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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