Nets of quadric surfaces and plane cubics and their GIT stability
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912972573507584 |
|---|---|
| author | Hattori, Masafumi Papazachariou, Theodoros Stylianos Zanardini, Aline |
| author_facet | Hattori, Masafumi Papazachariou, Theodoros Stylianos Zanardini, Aline |
| contents | A general net of quadric surfaces, together with a choice of a base point, defines a net of plane cubics via the Gale transformation of the remaining seven base points. To both nets, one can also naturally associate the same smooth plane quartic. In this paper, we generalize the cycle of correspondences arising from nets of quadrics that define rational elliptic threefolds and provide a complete criterion for GIT stability of the three underlying geometric objects using birational-geometric techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nets of quadric surfaces and plane cubics and their GIT stability Hattori, Masafumi Papazachariou, Theodoros Stylianos Zanardini, Aline Algebraic Geometry 14L24 (primary), 14C21, 14J27, 14E99, 14D06 (secondary) A general net of quadric surfaces, together with a choice of a base point, defines a net of plane cubics via the Gale transformation of the remaining seven base points. To both nets, one can also naturally associate the same smooth plane quartic. In this paper, we generalize the cycle of correspondences arising from nets of quadrics that define rational elliptic threefolds and provide a complete criterion for GIT stability of the three underlying geometric objects using birational-geometric techniques. |
| title | Nets of quadric surfaces and plane cubics and their GIT stability |
| topic | Algebraic Geometry 14L24 (primary), 14C21, 14J27, 14E99, 14D06 (secondary) |
| url | https://arxiv.org/abs/2603.17521 |