Bogomolov-Gieseker-type inequality and counting invariants
نویسندگان
چکیده
منابع مشابه
Arithmetic Bogomolov-gieseker’s Inequality
Let f : X → Spec(Z) be an arithmetic variety of dimension d ≥ 2 and (H, k) an arithmetically ample Hermitian line bundle on X, that is, a Hermitian line bundle with the following properties: (1) H is f -ample. (2) The Chern form c1(H∞, k) gives a Kähler form on X∞. (3) For every irreducible horizontal subvariety Y (i.e. Y is flat over Spec(Z)), the height ĉ1( (H, k)|Y ) dim Y of Y is positive. ...
متن کاملInequality of Bogomolov-gieseker’s Type on Arithmetic Surfaces
Let K be an algebraic number field, OK the ring of integers of K, and f : X → Spec(OK) an arithmetic surface. Let (E, h) be a rank r Hermitian vector bundle on X such that E Q is semistable on the geometric generic fiber X Q of f . In this paper, we will prove an arithmetic analogy of Bogomolov-Gieseker’s inequality: ĉ2(E, h)− r − 1 2r ĉ1(E, h) 2 ≥ 0. Table of
متن کاملConstructing and Counting Phylogenetic Invariants
The method of invariants is an approach to the problem of reconstructing the phylogenetic tree of a collection of m taxa using nucleotide sequence data. Models for the respective probabilities of the 4m possible vectors of bases at a given site will have unknown parameters that describe the random mechanism by which substitution occurs along the branches of a putative phylogenetic tree. An inva...
متن کاملA quantitative sharpening of Moriwaki’s arithmetic Bogomolov inequality
A. Moriwaki proved the following arithmetic analogue of the Bogomolov unstability theorem. If a torsion-free hermitian coherent sheaf on an arithmetic surface has negative discriminant then it admits an arithmetically destabilising subsheaf. In the geometric situation it is known that such a subsheaf can be found subject to an additional numerical constraint and here we prove the arithmetic ana...
متن کاملA Bogomolov Type Statement for Function Fields
Let k be a an algebraically closed field of arbitrary characteristic, and we let h : A(k(t)) −→ R≥0 be the usual Weil height for the n-dimensional affine space corresponding to the function field k(t) (extended to its algebraic closure). We prove that for any affine variety V ⊂ A defined over k(t), there exists a positive real number ε := ε(V ) such that if P ∈ V (k(t)) and h(P ) < ε, then P ∈ ...
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: Journal of Topology
سال: 2012
ISSN: 1753-8416
DOI: 10.1112/jtopol/jts037