|
| | | | |
| | | |
| Stat |
Members: 3665
Articles: 2'599'751
Articles rated: 2609
25 January 2025 |
|
| | | | |
|
Article overview
| |
|
|
Monodromy and Period Map of the Winger Pencil II: $E$-part | | Yunpeng Zi
; | | Date: |
2 Jan 2023 | | Abstract: | The sextic plane curves that are invariant under the standard action of the
icosahedral group on the projective plane make up a pencil of genus ten curves
(spanned by a sum of six lines and a three times a conic). This pencil was
first considered in a note by R.~M.~Winger in 1925 and is nowadays named after
him.
We gave this a modern treatment and proved among other things that it
contains essentially every smooth genus ten curve with icosahedral symmetry.
We here consider the monodromy group and the period map naturally defined by
the icosahedral symmetry. We showed that this monodromy group is a normal
subgroup of finite index in $SL_2(ds[sqrt{5}])$ and the period map brings
the Winger pencil to a curve on the Hilbert modular surface
$SL_2(ds[sqrt{5}])/Hds^2$. | | Source: | arXiv, 2301.00500 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|
REGISTER