Mathematics – Complex Variables
Scientific paper
2009-09-27
Mathematics
Complex Variables
Second draft, 17 pages
Scientific paper
Let $X$ be a general cyclic cover of $\mathbb{CP}^{1}$ ramified at $m$ points, $\lambda_1...\lambda_m.$ we define a class of non positive divisors on $X$ of degree $g-1$ supported in the pre images of the branch points on $X$, such that the the standard theta function doesn't vanish on their image in $J(X).$ These divisors generalize the divisors introduced in [BR] and [Na]. Generalizing the results of [BR],[Na] and [EG] we show that up to a certain determinant of the non standard periods of $X$, the value of the theta functions at these divisors is a polynomial in the branch point of the curve $X.$ Our treatment is based on a generalization of Accola's results of the 3 cyclic sheeted cover [Ac1] and a straightforward generalization of Nakayashiki's approach explained in [Na] in the non singular case for any singular cyclic cover.
No associations
LandOfFree
General cyclic covers and their Thomae formula 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 General cyclic covers and their Thomae formula, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and General cyclic covers and their Thomae formula will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-234331