Orbifold modifications of complex analytic varieties
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918262175956992 |
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| author | Ou, Wenhao |
| author_facet | Ou, Wenhao |
| contents | We prove that if $X$ is a compact complex analytic variety, which has quotient singularities in codimension 2, then there is a projective bimeromorphic morphism $f\colon Y\to X$, such that $Y$ has quotient singularities, and that the indeterminacy locus of $f^{-1}$ has codimension at least 3 in $X$. As an application, we deduce the Bogomolov-Gieseker inequality on orbifold Chern classes for stable reflexive coherent sheaves on compact Kähler varieties which have quotient singularities in codimension 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07273 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orbifold modifications of complex analytic varieties Ou, Wenhao Algebraic Geometry Complex Variables We prove that if $X$ is a compact complex analytic variety, which has quotient singularities in codimension 2, then there is a projective bimeromorphic morphism $f\colon Y\to X$, such that $Y$ has quotient singularities, and that the indeterminacy locus of $f^{-1}$ has codimension at least 3 in $X$. As an application, we deduce the Bogomolov-Gieseker inequality on orbifold Chern classes for stable reflexive coherent sheaves on compact Kähler varieties which have quotient singularities in codimension 2. |
| title | Orbifold modifications of complex analytic varieties |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2401.07273 |