Weierstrass points on cyclic covers of the projective line
نویسندگان
چکیده
منابع مشابه
Cyclic Covers of the Projective Line, Their Jacobians and Endomorphisms
ζp ∈ C. Let Q(ζp) be the pth cyclotomic field. It is well-known that Q(ζp) is a CM-field. If p is a Fermat prime then the only CM-subfield of Q(ζp) is Q(ζp) itself, since the Galois group of Q(ζp)/Q is a cyclic 2-group, whose only element of order 2 acts as the complex conjugation. All other subfields of Q(ζp) are totally real. Let f(x) ∈ C[x] be a polynomial of degree n ≥ 5 without multiple ro...
متن کاملThe Rank of the Cartier Operator on Cyclic Covers of the Projective Line
We give a lower bound on the rank of the Cartier operator of Jacobian varieties of hyperelliptic and superelliptic curves in terms of their genus.
متن کاملCounting Rational Points on Smooth Cyclic Covers
A conjecture of Serre concerns the number of rational points of bounded height on a finite cover of projective space Pn−1. In this paper, we achieve Serre’s conjecture in the special case of smooth cyclic covers of any degree when n ≥ 10, and surpass it for covers of degree r ≥ 3 when n > 10. This is achieved by a new bound for the number of perfect r-th power values of a polynomial with nonsin...
متن کاملTwelve Points on the Projective Line, Branched Covers, and Rational Elliptic Fibrations
The following divisors in the space Sym12 P1 of twelve points on P 1 are actually the same: (A) The possible locus of the twelve nodal fibers in a rational elliptic fibration (i.e. a pencil of plane cubic curves); (B) degree 12 binary forms that can be expressed as a cube plus a square; (C) the locus of the twelve tangents to a smooth plane quartic from a general point of the plane; (D) the bra...
متن کاملThe Endomorphism Rings of Jacobians of Cyclic Covers of the Projective Line
Suppose K is a eld of characteristic 0, Ka is its algebraic closure, p is an odd prime. Suppose, f(x) 2 K[x] is a polynomial of degree n 5 without multiple roots. Let us consider a curve C : y = f(x) and its jacobian J(C). It is known that the ring End(J(C)) of all Ka-endomorphisms of J(C) contains the ring Z[ p] of integers in the pth cyclotomic eld (generated by obvious automorphisms of C). W...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1996
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-96-01649-2