Smoothing low-dimensional algebraic cycles [after Kollár and Voisin]
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929410327707648 |
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| author | Benoist, Olivier |
| author_facet | Benoist, Olivier |
| contents | Let $X$ be a smooth projective complex algebraic variety. An old question of Borel and Haefliger asks whether any (possibly singular) algebraic subvariety of $X$ is homologically equivalent to a linear combination with integral coefficients of smooth algebraic subvarieties of $X$. In general, this question is too optimistic, and counterexamples have been known for a long time. The aim of this survey is to explain how János Kollár and Claire Voisin have provided a positive answer to Borel and Haefliger's question, for subvarieties of dimension less than half the dimension of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smoothing low-dimensional algebraic cycles [after Kollár and Voisin] Benoist, Olivier Algebraic Geometry 14C25 Let $X$ be a smooth projective complex algebraic variety. An old question of Borel and Haefliger asks whether any (possibly singular) algebraic subvariety of $X$ is homologically equivalent to a linear combination with integral coefficients of smooth algebraic subvarieties of $X$. In general, this question is too optimistic, and counterexamples have been known for a long time. The aim of this survey is to explain how János Kollár and Claire Voisin have provided a positive answer to Borel and Haefliger's question, for subvarieties of dimension less than half the dimension of $X$. |
| title | Smoothing low-dimensional algebraic cycles [after Kollár and Voisin] |
| topic | Algebraic Geometry 14C25 |
| url | https://arxiv.org/abs/2407.04000 |