Sigma Functions for Telescopic Curves
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2012
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914213104975872 |
|---|---|
| author | Ayano, Takanori |
| author_facet | Ayano, Takanori |
| contents | In this paper, we consider the sigma functions for algebraic curves expressed by a canonical form using a finite sequence $(a_1,...,a_t)$ of positive integers whose greatest common divisor is equal to one (Miura [13]). The idea is to express a non-singular algebraic curve by affine equations of $t$ variables whose orders at infinity are $(a_1,...,a_t)$. We construct a symplectic basis of the first cohomology group and the sigma functions for telescopic curves, i.e., the curves such that the number of defining equations is exactly $t-1$ in the Miura canonical form. The largest class of curves for which such construction has been obtained thus far is $(n,s)$-curves ([3][15]), which are telescopic because they are expressed in the Miura canonical form with $t=2$, $a_1=n$, and $a_2=s$, and the number of defining equations is one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1201_0644 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Sigma Functions for Telescopic Curves Ayano, Takanori Algebraic Geometry 14H55, 14H42, 14H50 In this paper, we consider the sigma functions for algebraic curves expressed by a canonical form using a finite sequence $(a_1,...,a_t)$ of positive integers whose greatest common divisor is equal to one (Miura [13]). The idea is to express a non-singular algebraic curve by affine equations of $t$ variables whose orders at infinity are $(a_1,...,a_t)$. We construct a symplectic basis of the first cohomology group and the sigma functions for telescopic curves, i.e., the curves such that the number of defining equations is exactly $t-1$ in the Miura canonical form. The largest class of curves for which such construction has been obtained thus far is $(n,s)$-curves ([3][15]), which are telescopic because they are expressed in the Miura canonical form with $t=2$, $a_1=n$, and $a_2=s$, and the number of defining equations is one. |
| title | Sigma Functions for Telescopic Curves |
| topic | Algebraic Geometry 14H55, 14H42, 14H50 |
| url | https://arxiv.org/abs/1201.0644 |