Characters and cohomology of modules for affine KacMoody algebras and generalizat...
Motivic cohomology and characterizations of the BlochKato conjecture
Full text  
Author(s): 
Total Authors: 3

Affiliation:  ^{[1]} Polish Acad Sci, Inst Matemat, PL00956 Warsaw  Poland
^{[2]} Warsaw Univ Sci & Technol, Wydzial Matemat & Nauk Informacyjnych, PL00661 Warsaw  Poland
^{[3]} Univ Sao Paulo, ICMC, Dept Matemat, BR13560970 Sao Carlos, SP  Brazil
Total Affiliations: 3

Document type:  Journal article 
Source:  ASIAN JOURNAL OF MATHEMATICS; v. 18, n. 3, p. 525544, 2014. 
Web of Science Citations:  0 
Abstract  
Let X, Y subset of k(m) (k = R, C) be smooth manifolds. We investigate the central symmetry of the configuration of X and Y. For p is an element of k(m) we introduce a number mu(p) of pairs of points x is an element of X and y is an element of Y such that p is the center of the interval (xy) over bar. We show that if X, Y (including the case X = Y) are algebraic manifolds in a general position, then there is a closed (semialgebraic) set B subset of k(m), called symmetry defect set of the X and Y configuration, such that the function mu is locally constant and not identically zero outside B. If k = C, we estimate the number mu (in fact we compute it in many cases) and show that the symmetry defect is an algebraic hypersurface and consequently the function mu is constant and positive outside B. We also show that in the generic case the topological type of the symmetry defect set of a plane curve is constant, i.e. the symmetry defect sets for two generic curves of the same degree are homeomorphic (by the same method we can prove similar statement for any irreducible family of smooth varieties Z(n) subset of C2n). Moreover, for k = R, we estimate the number of connected components of the set U = k(m) \textbackslash{} B. In the last section we give an algorithm to compute the symmetry defect set for complex smooth affine varieties in general position. (AU)  
FAPESP's process:  08/542226  Singularities, geometry and differential equations 
Grantee:  Maria Aparecida Soares Ruas 
Support type:  Research Projects  Thematic Grants 