Mathematics – Algebraic Geometry
Scientific paper
2012-01-03
Mathematics
Algebraic Geometry
22 pages
Scientific paper
In this paper, we consider a symplectic basis of the first cohomology group and 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.
No associations
LandOfFree
Sigma Functions for Telescopic Curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Sigma Functions for Telescopic Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sigma Functions for Telescopic Curves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-183879