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On Kähler-Einstein fake weighted projective spaces
- Author(s)
- 윤영한
- Advisor
- 황동선
- Department
- 일반대학원 수학과
- Publisher
- The Graduate School, Ajou University
- Publication Year
- 2021-02
- Language
- eng
- 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.
- Alternative Abstract
- 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.
- Fulltext
- Appears in Collections:
- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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