A real viewpoint on the intersection of complex quadrics and its topology
Algebraic Geometry
2011-06-10 v1 Algebraic Topology
Abstract
We study the relation between a complex projective set C in CP^n and the set R in RP^(2n+1) defined by viewing each equation of C as a pair of real equations. Once C is presented by quadratic equations, we can apply a spectral sequence to efficiently compute the homology of R; using the fact that the (Z_2)-cohomology of R is a free H*(C)-module with two generators we can in principle reconstruct the homology of C. Explicit computations for the intersection of two complex quadrics are presented.
Cite
@article{arxiv.1106.1828,
title = {A real viewpoint on the intersection of complex quadrics and its topology},
author = {Antonio Lerario},
journal= {arXiv preprint arXiv:1106.1828},
year = {2011}
}