Nodal surfaces with obstructed deformations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866913551642263552 |
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| author | Kloosterman, Remke |
| author_facet | Kloosterman, Remke |
| contents | In this text we show that the deformation space of a nodal surface $X$ of degree $d$ is smooth and of the expected dimension if $d\leq 7$ or $d\geq 8$ and $X$ has at most $4d-5$ nodes. (The case $d\leq 7$ was previously covered by Alexandru Dimca by using different techniques.)
For $d\geq 8$ we give explicit examples of nodal surfaces with $4d-4$ nodes, for which the tangent space to the deformation space has larger dimension than expected.
We give a short discussion on the shape of the deformation space of surfaces of the form $f_1f_2+f_3^2f_4$, where $f_1$ is a linear form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1612_06726 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Nodal surfaces with obstructed deformations Kloosterman, Remke Algebraic Geometry In this text we show that the deformation space of a nodal surface $X$ of degree $d$ is smooth and of the expected dimension if $d\leq 7$ or $d\geq 8$ and $X$ has at most $4d-5$ nodes. (The case $d\leq 7$ was previously covered by Alexandru Dimca by using different techniques.) For $d\geq 8$ we give explicit examples of nodal surfaces with $4d-4$ nodes, for which the tangent space to the deformation space has larger dimension than expected. We give a short discussion on the shape of the deformation space of surfaces of the form $f_1f_2+f_3^2f_4$, where $f_1$ is a linear form. |
| title | Nodal surfaces with obstructed deformations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1612.06726 |