Holomorphic forms in Г⧹G̸K and chern classes

Chow Homology and Chern Classes

Stringy Chern classes

Work of Dixon, Harvey, Vafa and Witten in the 80’s ([DHVW85]) introduced a notion of Euler characteristic (for quotients of a torus by a finite group) which became known as the physicist’s orbifold Euler number. In the 90’s V. Batyrev introduced a notion of stringy Euler number ([Bat99b]) for ‘arbitrary Kawamata log-terminal pairs’, proving that this number agrees with the physicist’s orbifold ...

Higgs Bundles and Holomorphic Forms

For a complex manifold X which has a holomorphic form ̟ of odd degree k, we endow E = ⊕ p≥a Λ (p,0)(X) with a Higgs bundle structure θ given by θ(Z)(φ) := {i(Z)̟} ∧ φ. The properties such as curvature and stability of these and other Higgs bundles are examined. We prove (Theorem 2, section 2, for k > 1) E and additional classes of Higgs subbundles of E do not admit Higgs-Hermitian-Yang-Mills metr...

Holomorphic Almost Modular Forms

Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in SL(2,Z). It is proved that such functions have a rotation-invariant limit distribution when the argument approaches the real axis. An example for a holomorphic almost modular form is...

Chern Character in Twisted K-theory: Equivariant and Holomorphic Cases

It was argued in [25], [5] that in the presence of a nontrivial Bfield, D-brane charges in type IIB string theories are classified by twisted Ktheory. In [4], it was proved that twisted K-theory is canonically isomorphic to bundle gerbe K-theory, whose elements are ordinary Hilbert bundles on a principal projective unitary bundle, with an action of the bundle gerbe determined by the principal p...