Rhetorikikonographie

Abstract

The moduli space of stable rational curves with marked points has two distinguished families of maps: the forgetful maps, given by forgetting some of the markings, and the Kapranov maps, given by complete linear series of ψ-classes. The collection of all these maps embeds the moduli space into a product of projective spaces. We call the multidegrees of this embedding "Kapranov degrees," which include as special cases the work of Witten, Silversmith, Castravet-Tevelev, Postnikov, Cavalieri-Gillespie-Monin, and Gillespie-Griffins-Levinson. We establish, in terms of a combinatorial matching condition, upper bounds for Kapranov degrees and a characterization of their positivity. The positivity characterization answers a question of Silversmith. We achieve this by proving a recursive formula for Kapranov degrees and by using tools from the theory of error correcting codes.