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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1709.07398 |
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| _version_ | 1866914628865359872 |
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| author | Chen, Jingshan Chen, Yongchang |
| author_facet | Chen, Jingshan Chen, Yongchang |
| contents | In this paper, we show that the $Δ$-genus $Δ(X,\mathcal{L})\ge 0$ for any connected polarized demi-normal scheme $(X,\mathcal{L})$. As an application, we obtain $Δ(X,I(K_X+Λ))\ge 0$ for any KSBA stable log scheme $(X,Λ)$, where $I$ is the Cartier index of $K_X+Λ$. We also construct examples of KSBA stable log schemes with $I=1$ and $Δ(X,K_X+Λ)= 0$, which shows the inequality is sharp when $I=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_07398 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Positivity of $Δ$-genera for connected polarized demi-normal schemes Chen, Jingshan Chen, Yongchang Algebraic Geometry 14C20(Primary), 14J10(Secondary) In this paper, we show that the $Δ$-genus $Δ(X,\mathcal{L})\ge 0$ for any connected polarized demi-normal scheme $(X,\mathcal{L})$. As an application, we obtain $Δ(X,I(K_X+Λ))\ge 0$ for any KSBA stable log scheme $(X,Λ)$, where $I$ is the Cartier index of $K_X+Λ$. We also construct examples of KSBA stable log schemes with $I=1$ and $Δ(X,K_X+Λ)= 0$, which shows the inequality is sharp when $I=1$. |
| title | Positivity of $Δ$-genera for connected polarized demi-normal schemes |
| topic | Algebraic Geometry 14C20(Primary), 14J10(Secondary) |
| url | https://arxiv.org/abs/1709.07398 |