A semi-dualizing module over a commutative noetherian ringA is a finitely generated module C with RHomA(C,C) ≃ A in the derived category D(A). We show how each such module gives rise to three new homological dimensions which we call C–Gorenstein projective, C–Gorenstein injective, and C–Gorenstein flat dimension, and investigate the properties of these dimensions.

This paper announces results on the behavior of some important algebraic and topological invariants — Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. — and their associated characteristic classes, under morphisms of projective algebraic varieties. The formulas obtained relate global invariants to singularities of general complex algebraic (...

There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves $I$-invariant projective vector fields. The sub-algebra $C$-projective fields, leaving $H$-curvature invariant, has been studied extensively. Here on a closed Finsler space with negative definite Ricci curvature reduces to that Killing Moreover, if an admits such...

Let X be a normal projective variety admitting an action of a semisimple group with a unique closed orbit. We construct finitely many rational curves in X , all having a common point, such that every effective one–cycle on X is rationally equivalent to a unique linear combination of these curves with non–negative rational coefficients. When X is nonsingular, these curves are projective lines, a...

We address the problem of the continuum limit for a system of Hausdorr lattices (namely lattices of isolated points) approximating a topological space M. The correct framework is that of projective systems. The projective limit is a universal space from which M can be recovered as a quotient. We dualize the construction to approximate the algebra C(M) of continuous functions on M. In a companio...

We investigate the differential calculus defined by Ashtekar and Lewandowski on projective limits of manifolds by means of cylindrical smooth functions and compare it with the C calculus proposed by Fröhlicher and Kriegl in more general context. For products of connected manifolds, a Boman theorem is proved, showing the equivalence of the two calculi in this particular case. Several examples of...

The SL2R Lie-group consists of the real 2× 2 matrices ( d b c a ) with unit determinant ad − cb = 1. The S̃L2R geometry is the universal covering group of this group, and is a Lie-group itself. Because of the 3 independent coordinates, S̃L2R is a 3-dimensional manifold, with its usual neighbourhood topology. In order to model the above structure on the projective sphere PS3 and space P3 we introd...