ar X iv : m at h / 01 05 09 8 v 1 [ m at h . A G ] 1 1 M ay 2 00 1 A fixed point formula of Lefschetz type

ar X iv : 0 70 8 . 42 79 v 2 [ m at h . K T ] 2 9 M ay 2 00 8 A LEFSCHETZ FIXED - POINT FORMULA FOR CERTAIN ORBIFOLD C * - ALGEBRAS

Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of crossed product C-algebras C0(X)⋊ G coming from covariant pairs. Here G is assumed countable, X a manifold, and X ⋊ G cocompact and proper. The formula in question expresses the graded trace of the map on rationalized K-theory of C0(X) ⋊ G induced by the endomorphism, i.e. the Lefschetz n...

ar X iv : m at h / 04 05 40 1 v 1 [ m at h . G N ] 2 1 M ay 2 00 4 VARIATIONS ON KURATOWSKI ’ S 14 - SET THEOREM

Kuratowski’s 14-set theorem says that in a topological space, 14 is the maximum possible number of distinct sets which can be generated from a fixed set by taking closures and complements. In this article we consider the analogous questions for any possible subcollection of the operations {closure, complement, interior, intersection, union}, and any number of initially given sets. We use the al...

ar X iv : m at h / 01 05 15 1 v 1 [ m at h . A C ] 1 7 M ay 2 00 1 The Hilbert Series of Pfaffian Rings ⋆

We give three determinantal expressions for the Hilbert series as well as the Hilbert function of a Pfaffian ring, and a closed form product formula for its multiplicity. An appendix outlining some basic facts about degeneracy loci and applications to multiplicity formulae for Pfaffian rings is also included.

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h / 01 05 23 2 v 1 [ m at h . N T ] 2 8 M ay 2 00 1 MODULAR CURVES OF GENUS 2

We prove that there are exactly 149 genus two curves C defined over Q such that there exists a nonconstant morphism π : X 1 (N) → C defined over Q and the jacobian of C is Q-isogenous to the abelian variety A f attached by Shimura to a newform f ∈ S 2 (Γ 1 (N)). We determine the corresponding newforms and present equations for all these curves.