Stability of Arakelov Bundles and Tensor Products without Global Sections
نویسندگان
چکیده
This paper deals with Arakelov vector bundles over an arithmetic curve, i.e. over the set of places of a number field. The main result is that for each semistable bundle E, there is a bundle F such that E⊗F has at least a certain slope, but no global sections. It is motivated by an analogous theorem of Faltings for vector bundles over algebraic curves and contains the Minkowski-Hlawka theorem on sphere packings as a special case. The proof uses an adelic version of Siegel’s mean value formula. 2000 Mathematics Subject Classification: Primary 14G40; Secondary 11H31, 11R56.
منابع مشابه
Concerning the semistability of tensor products in Arakelov geometry
— We study the semistability of the tensor product of hermitian vector bundles by using the ε-tensor product and the geometric (semi)stability of vector subspaces in the tensor product of two vector spaces. Notably, for any number field K and any hermitian vector bundles E and F over SpecOK , we show that the maximal slopes of E, F , and E ⊗ F satisfy the following inequality : μ̂max(E ⊗ F ) 6 μ̂...
متن کاملar X iv : h ep - t h / 02 03 17 4 v 1 1 9 M ar 2 00 2 ON DECOMPOSING N = 2 LINE BUNDLES AS TENSOR PRODUCTS OF N = 1 LINE BUNDLES
We obtain the existence of a cohomological obstruction to expressing N = 2 line bundles as tensor products of N = 1 bundles. The motivation behind this paper is an attempt at understanding the N = 2 super KP equation via Baker functions, which are special sections of line bundles on supercurves. There has been—for some time now (cf. [DG])—an interest in extending the study of the super KP equat...
متن کاملTensor Algebras, Symmetric Algebras and Exterior Algebras
We begin by defining tensor products of vector spaces over a field and then we investigate some basic properties of these tensors, in particular the existence of bases and duality. After this, we investigate special kinds of tensors, namely, symmetric tensors and skew-symmetric tensors. Tensor products of modules over a commutative ring with identity will be discussed very briefly. They show up...
متن کاملEffectivity of Arakelov Divisors and the Theta Divisor of a Number Field
In the well known analogy between the theory of function fields of curves over finite fields and the arithmetic of algebraic number fields, the number theoretical analogue of a divisor on a curve is an Arakelov divisor. In this paper we introduce the notion of an effective Arakelov divisor; more precisely, we attach to every Arakelov divisor D its effectivity, a real number between 0 and 1. Thi...
متن کاملGlobal Sections of Some Vector Bundles on Kontsevich Moduli Spaces
On the Kontsevich moduli space of unpointed stable maps to P1 of genus 0 and degree e, there is a tautological vector bundle of rank e − 1. Global sections of tensor powers of this vector bundle arise when considering holomorphic contravariant tensors on Kontsevich spaces of stable maps to more general projective varieties. The computation of the global sections is reduced to an explicit combin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003