Topology and arithmetic of resultants, I: spaces of rational maps
Abstract
We consider the interplay of point counts, singular cohomology, étale cohomology, eigenvalues of the Frobenius and the Grothendieck ring of varieties for two families of varieties: spaces of rational maps and moduli spaces of marked, degree $d$ rational curves in $\mathbb{P}^n$. We deduce as special cases algebrogeometric and arithmetic refinements of topological computations of Segal, CohenCohenMannMilgram, Vassiliev and others.
 Publication:

arXiv eprints
 Pub Date:
 June 2015
 arXiv:
 arXiv:1506.02713
 Bibcode:
 2015arXiv150602713F
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology;
 Mathematics  Geometric Topology;
 Mathematics  Number Theory
 EPrint:
 Corrected mistake in proof of Theorem 1.2 (leading to minor change in statement of theorem). Updated intro to note that Question 1.4 has been answered in negative by H. Spink and D. Tseng