The motivic class of the space of genus 0 maps to the flag variety
2026/01/12 by Jim Bryan, Balázs Elek, Freddie Manners +2 · 4 voices · 1 citation
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Abstract
Let Fln+1 be the variety of complete flags in \mathbbAn+1 and let Ω2β(Fln+1) be the space of based maps f:ℙ1→ Fln+1 in the class f*[ℙ1]=β. We show that under a mild positivity condition on β, the class of Ω2β(Fln+1) in K0(Var), the Grothendieck group of varieties, is given by [Ω2β(Fln+1)] = [GLn× \mathbbAa]. The proof of this result was obtained in conjunction with Google Gemini and related tools. We briefly discuss this research interaction, which may be of independent interest. However, the treatment in this paper is entirely human-authored (aside from excerpts in an appendix which are clearly marked as such).
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