The Isomorphism Classes of the Surfaces $x_1^{a_1} + x_2^{a_2} + x_3^{a_3} + 1 = 0$
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917472299384832 |
|---|---|
| author | Chitayat, Michael Hajra, Buddhadev |
| author_facet | Chitayat, Michael Hajra, Buddhadev |
| contents | Let $f = x_1^{a_1} + x_2^{a_2} + x_3^{a_3} + 1 \in \mathbb{C}[x_1,x_2,x_3]$ and let $g = y_1^{b_1} + y_2^{b_2} + y_3^{b_3} + 1 \in \mathbb{C}[y_1,y_2,y_3]$ where $a_1,a_2,a_3,b_1,b_2,b_3 \geq 2$. We prove that the surfaces $V(f) \subset \mathbb{A}^3$ and $V(g) \subset \mathbb{A}^3$ are isomorphic if and only if $(a_1,a_2,a_3) = (b_1,b_2,b_3)$ up to a permutation of the entries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07617 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Isomorphism Classes of the Surfaces $x_1^{a_1} + x_2^{a_2} + x_3^{a_3} + 1 = 0$ Chitayat, Michael Hajra, Buddhadev Algebraic Geometry Commutative Algebra 14J10, 14J70, 14R05, 14R25 Let $f = x_1^{a_1} + x_2^{a_2} + x_3^{a_3} + 1 \in \mathbb{C}[x_1,x_2,x_3]$ and let $g = y_1^{b_1} + y_2^{b_2} + y_3^{b_3} + 1 \in \mathbb{C}[y_1,y_2,y_3]$ where $a_1,a_2,a_3,b_1,b_2,b_3 \geq 2$. We prove that the surfaces $V(f) \subset \mathbb{A}^3$ and $V(g) \subset \mathbb{A}^3$ are isomorphic if and only if $(a_1,a_2,a_3) = (b_1,b_2,b_3)$ up to a permutation of the entries. |
| title | The Isomorphism Classes of the Surfaces $x_1^{a_1} + x_2^{a_2} + x_3^{a_3} + 1 = 0$ |
| topic | Algebraic Geometry Commutative Algebra 14J10, 14J70, 14R05, 14R25 |
| url | https://arxiv.org/abs/2605.07617 |