منابع مشابه
Deforming Curves in Jacobians to Non-Jacobians II: Curves
We introduce deformation theoretic methods for determining when a curve X in a nonhyperelliptic Jacobian JC will deform with JC to a non-Jacobian. We apply these methods to a particular class of curves in symmetric powers C of C where 3 e g−3. More precisely, given a pencil g1 d of degree d on C, let X be the curve parametrizing divisors of degree e in divisors of g1 d (see the paper for the pr...
متن کاملAlgorithmic Aspects of Hyperelliptic Curves and their Jacobians
English) The contribution of this thesis is divided naturally into two parts. In Part I we generalise the work of Khuri-Makdisi [22] on algorithms for divisor arithmetic on curves over fields to more general bases. We prove that the natural analogues of the results of Khuri-Makdisi [22] continue to hold for relative effective Cartier divisors on projective schemes which are smooth of relative d...
متن کاملCurves in Jacobians to Non - Jacobians Ii
This is a second paper where we introduce deformation theory methods which can be applied to finding curves in families of principally polarized abelian varieties (ppav) containing jacobians. One of our motivations for finding interesting and computationally tractable curves in ppav is to solve the Hodge conjecture for the primitive cohomology of the theta divisor which we explain below. For ot...
متن کاملCurves , Jacobians , and Zeta Functions
When we speak about a function field of one variable over a field K, we mean a finitely generated regular extension F of K of transcendence degree 1. We briefly recall the definitions of the main objects attached to F/K and their properties. See the books [Che51] or [Sti93] for details. A more comprehensive survey can be found [FrJ08, Sections 3.1-3.2]. A K-place of F is a place φ: F → K̃ ∪ {∞} ...
متن کاملOn maps between modular Jacobians and Jacobians of Shimura curves
Fix a squarefree integer N , divisible by an even number of primes, and let Γ be a congruence subgroup of level M , where M is prime to N . For each D dividing N and divisible by an even number of primes, the Shimura curve X(Γ0(N/D)∩Γ ) associated to the indefinite quaternion algebra of discriminant D and Γ0(N/D) ∩ Γ -level structure is well defined, and we can consider its Jacobian J(Γ0(N/D) ∩...
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: Advances in Mathematics
سال: 1977
ISSN: 0001-8708
DOI: 10.1016/0001-8708(77)90067-6