Bounds for Chern classes of semistable vector bundles on complex projective spaces
نویسندگان
چکیده
منابع مشابه
On Semistable Principal Bundles over a Complex Projective Manifold, Ii
Let (X, ω) be a compact connected Kähler manifold of complex dimension d and EG −→ X a holomorphic principal G–bundle, where G is a connected reductive linear algebraic group defined over C. Let Z(G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P ⊂ G and a holomorphic reduction of structure group EP ⊂ EG to P , such that ...
متن کاملOn Semistable Principal Bundles over a Complex Projective Manifold
Let G be a simple linear algebraic group defined over the field of complex numbers. Fix a proper parabolic subgroup P of G, and also fix a nontrivial antidominant character χ of P . We prove that a holomorphic principal G–bundle EG over a connected complex projective manifold M is semistable satisfying the condition that the second Chern class c2(ad(EG)) ∈ H (M, Q) vanishes if and only if the l...
متن کاملChern classes of automorphic vector bundles
1.1. Suppose X is a compact n-dimensional complex manifold. Each partition I = {i1, i2, . . . , ir} of n corresponds to a Chern number c (X) = ǫ(c1(X)∪c2(X)∪. . .∪cr(X)∩[X]) ∈ Z where c(X) ∈ H(X;Z) are the Chern classes of the tangent bundle, [X] ∈ H2n(X;Z) is the fundamental class, and ǫ : H0(X;Z) → Z is the augmentation. Many invariants of X (such as its complex cobordism class) may be expres...
متن کاملHodge Style Chern Classes for Vector Bundles on Schemes
In this note, we develop the formalism of Hodge style chern classes of vector bundles over arbitrary quasi-projective schemes defined over K, a field of characteristic zero. The theory of Chern classes is well known by now and without any restriction on the characteristic, can be defined in many theories with rational coefficients, like for example the Chow ring. Atiyah [1] developed the theory...
متن کاملMirror Symmetry for Concavex Vector Bundles on Projective Spaces
Let V + = ⊕i∈IO(ki) and V − = ⊕j∈JO(−lj) be vector bundles on P s with ki and lj positive integers. Suppose X ι →֒ Ps is the zero locus of a generic section of V + and Y is a projective manifold such that X j →֒ Y with normal bundle NX/Y = ι ∗(V −). The relations between Gromov-Witten theories of X and Y are studied here by means of a suitably defined equivariant Gromov-Witten theory in Ps. We ap...
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: Colloquium Mathematicum
سال: 1993
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-65-2-277-290