Perspective and open problems on birational properties and singularities of moduli scheme of sheaves on surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917633689911296 |
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| author | Yamada, Kimiko |
| author_facet | Yamada, Kimiko |
| contents | For complex projective smooth surface $X$, let $M$ be the coarse moduli scheme of rank-two stable sheaves with fixed Chern classes. Grasping the birational structure of $M$, for example its Kodaira dimension, is a fundamental problem. However, in the case where $κ(X)>0$, the study of this problem has not necessarily been active in recent years. In this article we survey the study of this problem, especially for the case where $κ(X)=1$ and $c_1=0$. We will also survey some research on the structure of singularities of $M$, and a minimal model program of $M$. While explaining motivations, we raise several unsolved problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perspective and open problems on birational properties and singularities of moduli scheme of sheaves on surfaces Yamada, Kimiko Algebraic Geometry 14J60, 14D20, 32G13, 14B05, 14Exx For complex projective smooth surface $X$, let $M$ be the coarse moduli scheme of rank-two stable sheaves with fixed Chern classes. Grasping the birational structure of $M$, for example its Kodaira dimension, is a fundamental problem. However, in the case where $κ(X)>0$, the study of this problem has not necessarily been active in recent years. In this article we survey the study of this problem, especially for the case where $κ(X)=1$ and $c_1=0$. We will also survey some research on the structure of singularities of $M$, and a minimal model program of $M$. While explaining motivations, we raise several unsolved problems. |
| title | Perspective and open problems on birational properties and singularities of moduli scheme of sheaves on surfaces |
| topic | Algebraic Geometry 14J60, 14D20, 32G13, 14B05, 14Exx |
| url | https://arxiv.org/abs/2404.05549 |