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 algebro-geometric and arithmetic refinements of topological computations of Segal, Cohen--Cohen--Mann--Milgram, Vassiliev and others.

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

Cited by in corpus (3)

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• Topology and arithmetic of resultants, II: the resultant $=1$ hypersurface (with an appendix by C. Cazanave)
• The homotopy type of spaces of resultants of bounded multiplicity