Ranks of homotopy and cohomology groups for rationally elliptic spaces and algebraic varieties

Rationally Connected Varieties and Loop Spaces

We consider rationally connected complex projective manifolds M and show that their loop spaces—infinite dimensional complex manifolds—have properties similar to those of M . Furthermore, we give a finite dimensional application concerning holomorphic vector bundles over rationally connected complex projective manifolds. 0 Introduction LetM be a complex manifold and r = 0, 1, . . . ,∞. The spac...

Rationally connected varieties and fundamental groups

On a rationally connected variety we would like to use rational curves to obtain a similar result. Complete intersection curves are essentially never rational. (For instance, if X ⊂ P is a hypersurface then a general complete intersection with hyperplanes is rational iff X is a hyperplane or a quadric.) Therefore we have to proceed in a quite different way. Let X be a smooth, projective, ration...

Cohomology of Algebraic Spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

An intrinsic homotopy for intersecting algebraic varieties

Recently we developed a diagonal homotopy method to compute a numerical representation of all positive dimensional components in the intersection of two irreducible algebraic sets. In this paper, we rewrite this diagonal homotopy in intrinsic coordinates, which reduces the number of variables, typically in half. This has the potential to save a significant amount of computation, especially in t...