In this paper we construct the analogue of Dedekind η−function on the moduli space of polarized CY manifolds. We prove that the L norm of η(τ ) is the regularized determinants of the Laplacians of the CY metric on (0, 1) forms. We construct the analogue of the Baily-Borel Compactification of the moduli space of polarized CY and prove that it has the same properties as the Baily-Borel compactifi...

We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson found in [And03] and [And06]. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system of equations for the components of a compactification of the given metric. This, together with boundary conditions that the com...

We formulate and describe a visual compactification of the Teichmüller space by Weil-Petersson geodesic rays emanating from a point X. We focus on analogies with Bers’s compactification: due to non-completeness, finite rays correspond to cusps, and such cusps are dense in the visual sphere. By analogy with a result of Kerckhoff and Thurston, we show the natural action of the mapping class group...

In a previous paper [K1] I have constructed a compactification KGLn of the general linear group GLn, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De Concini and Procesi. In particular there is an action of G = GLn × GLn on this compactification. In this paper we show how the space of global section of an arb...

1.2. Primer on Connections. Recall from Peng’s talk that a connection on P → X can be thought of in three ways: (1) As a field of horizontal subspaces: TpP = HpP⊕VpP , where V P = ker (π∗). (Note that Vp ∼= g, and Hp ∼= Tπ(p)X). (2) As a g-valued 1-form A ∈ ΩX (g) which is invariant w.r.t. the induced G-action on ΩX (g). (3) Given a representation of G on W , as a vector bundle connection on th...

A general formula is obtained for Yukawa couplings in compactification on Landau-Ginzburg orbifolds and corresponding Calabi-Yau spaces. Up to the kinetic term normalizations, this equates the classical Koszul ring structure with the LandauGinzburg orbifold chiral ring structure and the true superconformal field theory ring structure.

Introduction. In 1937 E. Čech and M.H. Stone independently introduced the maximal compactification of a completely regular topological space, thereafter called Stone-Čech compactification [8, 18]. In the introduction of [8] the non-constructive character of this result is so described: “it must be emphasized that β(S) [the Stone-Čech compactification of S] may be defined only formally (not cons...

We study structures called d-frames which were developed by the last two authors for a bitopological treatment of Stone duality. These structures consist of a pair of frames thought of as the opens of two topologies, together with two relations which serve as abstractions of disjointness and covering of the space. With these relations, the topological separation axioms regularity and normality ...

we characterize function spaces of rees matrixsemigroups. then we study these spaces by using the topologicaltensor product technique.