Symmetric and Kähler–Einstein Fano polygons
- 주제(키워드) Symmetric Fano polygon , Kähler–Einstein Fano polygon , B-transformation
- 발행기관 아주대학교
- 지도교수 황동선
- 발행년도 2020
- 학위수여년월 2020. 8
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/ajou/000000030222
- 본문언어 영어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
We investigate symmetric and Kähler–Einstein Fano polytopes mainly focusing on the two dimensional singular case. In particular, we construct some examples of symmetric but not Kähler–Einstein singular Fano polygons which cannot exist in the smooth case. In fact, we completely classified all such cases. We also show that symmetric and Kähler–Einstein Fano polygon admits a non-trivial rotation and construct examples of a Fano polygon that isKähler–Einstein but not symmetric. To understand more about Kähler–Einstein Fano polygons and symmetric Fano polygons, we introduce a new notion called the B-transformation of a Fano polygon. In particular, if a Fano polygon is symmetric or Kähler–Einstein then the B-transformation of the Fano polygon is also a Fano polygon. Then, we show that the property of being symmetric for Fano polygons is invariant under the B-transformation.
more목차
Introduction 1
Preliminaries 3
Symmetric and Kähler–Einstein Fano polygons 8
B-transformations 15
Further discussions 22
Bibliography 27
