Counting divisorial contractions with centre a $cA_n$-singularity
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866915471214772224 |
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| author | Paemurru, Erik |
| author_facet | Paemurru, Erik |
| contents | First, we simplify the existing classification due to Kawakita and Yamamoto of 3-dimensional divisorial contractions with centre a $cA_n$-singularity, also called compound $A_n$ singularity. Next, we describe the global algebraic divisorial contractions corresponding to a given local analytic equivalence class of divisorial contractions with centre a point. Finally, we consider divisorial contractions of discrepancy at least 2 to a fixed variety with centre a $cA_n$-singularity. We show that if there exists one such divisorial contraction, then there exist uncountably many such divisorial contractions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_08045 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Counting divisorial contractions with centre a $cA_n$-singularity Paemurru, Erik Algebraic Geometry 14E30 (Primary) 14E05, 14J30 (Secondary) First, we simplify the existing classification due to Kawakita and Yamamoto of 3-dimensional divisorial contractions with centre a $cA_n$-singularity, also called compound $A_n$ singularity. Next, we describe the global algebraic divisorial contractions corresponding to a given local analytic equivalence class of divisorial contractions with centre a point. Finally, we consider divisorial contractions of discrepancy at least 2 to a fixed variety with centre a $cA_n$-singularity. We show that if there exists one such divisorial contraction, then there exist uncountably many such divisorial contractions. |
| title | Counting divisorial contractions with centre a $cA_n$-singularity |
| topic | Algebraic Geometry 14E30 (Primary) 14E05, 14J30 (Secondary) |
| url | https://arxiv.org/abs/2204.08045 |