Komplexe R�ume

Kudla’s Modularity Conjecture and Formal Fourier–jacobi Series

“…⊂ Sp 2g (Z) on the above identity (15). The left-hand side is invariant in weight k and index n by the assumption on f .…”

“…Choosing holomorphic coordinates appropriately, we may assume that there is a small polycylinder U ⊂ W around a in which D 0 ∩ U = D ∩ U = {τ ∈ U : τ 1 = 0}. Then, according to Satz 10 and Hilfssatz 2 in Section 2.5 of [15], every irreducible component ofW ∩ p −1 1 (U ) is a winding covering, that is, isomorphic to a covering of the form {(τ, X ) : Proof. Without loss of generality we may assume that Q is irreducible.…”

Lattice Cohomology of Normal Surface Singularities

“…Notice thatX \ E ≈ X \{0} has the homotopy type of M , hence the abelianization map π 1 (X \ E) = π 1 (M ) → H defines a regular Galois covering ofX \ E. This has a unique extension p : Z → X with Z normal and p finite [5]. The (reduced) branch locus of p is included in E, and the Galois action of H extends to Z as well.…”

Boundary kernel functions for domains on complex manifolds

“…This can be proved as follows. By the closure of modules theorem [8] W)) which is multiplication by w is a homeomorphism whenever it is one-to-one; but for every point in U there is such a neighborhood and a suitable w since the functions on X separate points. In fact, we can choose w in such a way that w is different from zero in some neighborhood of a given point in U and thus avoid the use of the closure of modules theorem.…”