Minimal rational graphs admitting a QHD smoothing
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911693098975232 |
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| author | Beke, Márton |
| author_facet | Beke, Márton |
| contents | Using the picture deformation technique of De Jong-Van Straten we show that no singularity whose resolution graph has 3 or 4 large nodes, i.e., nodes satisfying d(v)+e(v)\leq -2, has a QHD smoothing. This is achieved by providing a general reduction algorithm for graphs with QHD smoothings, and enumeration. New examples and families are presented, which admit a combinatorial QHD smoothing, i.e. the incidence relations for a sandwich presentation can be satisfied. We also give a new proof of the Bhupal-Stipsicz theorem on the classification of weighted homogeneous singularities admitting QHD smoothings with this method by using cusp singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06929 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal rational graphs admitting a QHD smoothing Beke, Márton Geometric Topology Algebraic Geometry Using the picture deformation technique of De Jong-Van Straten we show that no singularity whose resolution graph has 3 or 4 large nodes, i.e., nodes satisfying d(v)+e(v)\leq -2, has a QHD smoothing. This is achieved by providing a general reduction algorithm for graphs with QHD smoothings, and enumeration. New examples and families are presented, which admit a combinatorial QHD smoothing, i.e. the incidence relations for a sandwich presentation can be satisfied. We also give a new proof of the Bhupal-Stipsicz theorem on the classification of weighted homogeneous singularities admitting QHD smoothings with this method by using cusp singularities. |
| title | Minimal rational graphs admitting a QHD smoothing |
| topic | Geometric Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2504.06929 |