let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

Abstract Answering a question of Hatcher and Vogtmann, we prove that the top homology group free factor complex is not dualizing module for $\operatorname {Aut}(F_{n})$, at least $n = 5$.

We try to determine the partition function of N = 4 ADE gauge theory on K3 by self-dualizing our previous ADE partition function. The resulting partition function satisfies gap condition.

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal sixmanifold M with static SU(2) structure and mirror M̂ , it is argued that the product M×M̂ is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and M̂ . The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric an...

In this paper it is proved that the volumes of the moduli spaces of polarized Calabi-Yau manifolds with respect to Weil-Petersson metrics are rational numbers. Mumford introduce the notion of a good metric on vector bundle over a quasi-projective variety in [10]. He proved that the Chern forms of good metrics define classes of cohomology with integer coefficients on the compactified quasi-proje...

Two distinguished types of semidualizing complexes are the shifts underlying rings and dualizing complexes. Let C be a complex for an analytically irreducible local ring R set n:=supC d:=dimRC. We show that is quasi-isomorphic to shift if only nth Betti number one. Also, we dth Bass