Singular set of some Kähler orbifolds

The T-singular Homology of Orbifolds

For an orbifold M we define a homology group, called t-singular homology group t-Hq(M), which depends not only on the topological structure of the underlying space of M , but also on the orbifold structure of M . We prove that it is a b-homotopy invariant of orbifolds. If M is a manifold, t-Hq(M) coincides with the usual singular homology group. We calculate the t-singular homology groups with ...

NOTES ON THE s-SINGULAR AND t-SINGULAR HOMOLOGIES OF ORBIFOLDS

In a preceding paper we have introduced the t-singular homology with integral coefficient of orbifolds, which captures the orbifold structures. In this paper we introduce the s-singular homology of orbifolds, and study the s-singular homology of orbifolds and the t-singular homology with rational coefficient of orbifolds. The main theorems are the following: (i) the s-singular homology group of...

Some Irrational Generalised Moonshine from Orbifolds

We verify the Generalised Moonshine conjectures for some irrational modular functions for the Monster centralisers related to the Harada-Norton, Held, M12 and L3(3) simple groups based on certain orbifolding constraints. We find explicitly the fixing groups of the hauptmoduls arising in each case. PACS: 11.25.Hf, 02.10.De, 02.20.Bb

Kähler (& Hyper-kähler) Manifolds

These notes are based on two talks given at the Arithmetic & Algebraic Geometry Seminar of the Korteweg-de Vriesinstituut for mathematics of the Universiteit van Amsterdam. They are intended to give a short introduction to the theory of Kähler manifolds, with a slight focus of applicability to the subject of K3 surfaces. However, they also include other interesting results not related to K3 sur...

Some Singular Mixed Problems.