Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve
نویسندگان
چکیده
منابع مشابه
Periodic Points on Veech Surfaces and the Mordell-weil Group over a Teichmüller Curve
Periodic points are points on Veech surfaces, whose orbit under the group of affine diffeomorphisms is finite. We characterise those points as being torsion points if the Veech surfaces is suitably mapped to its Jacobian or an appropriate factor thereof. For a primitive Veech surface in genus two we show that the only periodic points are the Weierstraß points and the singularities. Our main too...
متن کاملOn the Mordell–weil Group of the Elliptic Curve
We study an infinite family of Mordell curves (i.e. the elliptic curves in the form y = x + n, n ∈ Z) over Q with three explicit integral points. We show that the points are independent in certain cases. We describe how to compute bounds of the canonical heights of the points. Using the result we show that any pair in the three points can always be a part of a basis of the free part of the Mord...
متن کاملChabauty without the Mordell-weil Group
Based on ideas from recent joint work with Bjorn Poonen, we describe an algorithm that can in certain cases determine the set of rational points on a curve C, given only the p-Selmer group S of its Jacobian (or some other abelian variety C maps to) and the image of the p-Selmer set of C in S. The method is more likely to succeed when the genus is large, which is when it is usually rather diffic...
متن کاملElliptic Curves Group Law and Mordell-weil
This paper assumes no background on elliptic curves and culminates with a proof of the Mordell-Weil theorem. The Riemann-Roch and Dirichlet unit theorem are recalled but used without proof, but everything else is self-contained. After some elementary properties of elliptic curves are given, the group structure is explored in detail.
متن کاملSpecializations of Elliptic Surfaces, and Divisibility in the Mordell-weil Group
Let E → C be an elliptic surface, defined over a number field k, let P : C → E be a section, and let l be a rational prime. We bound the number of points of low algebraic degree in the l-division hull of P at the fibre Et. Specifically, for t ∈ C(k) with [k(t) : k] ≤ B1 such that Et is non-singular, we obtain a bound on the number of Q ∈ Et(k) such that [k(Q) : k] ≤ B2, and such that lQ = Pt, f...
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: Inventiones mathematicae
سال: 2006
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-006-0510-3