How to calculate homology groups of spaces of nonsingular algebraic projective hypersurfaces

Abstract

A general method of computing cohomology groups of the space of nonsingular algebraic hypersurfaces of degree $d$ in $C{P}^n$ is described. Using this method, rational cohomology groups of such spaces with $n=2,d\le 4$ and $n=3=d$ are calculated.

Cited by in corpus (7)

• Rational cohomology of the moduli space of trigonal curves of genus 5
• Decomposition in Coxeter-chambers of the configuration space of $d$ marked points on the complex plane
• Rational homology of the order complex of zero sets of homogeneous quadratic polynomial systems in $R^3$
• Homology groups of spaces of non-resultant quadratic polynomial systems in R^3
• Conical resolutions and cohomology of the moduli spaces of nodal hypersurfaces
• Rational cohomology of ${\mathcal{M}}_{4,1}$
• Topology of spaces of regular sections and applications to automorphism groups