2019/09/12 by Larson, Hannah, Vogt, Isabel
#14H50 #14N15 #14P25 #55M25 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1909.05945
Recent work of Kass--Wickelgren gives an enriched count of the 27 lines on a smooth cubic surface over arbitrary fields. Their approach using \mathbbA1-enumerative geometry suggests that other classical enumerative problems should have similar enrichments, when the answer is computed as the degree of the Euler class of a relatively orientable vector bundle. Here, we consider the closely related problem of the 28 bitangents to a smooth plane quartic. However, it turns out the relevant vector bundle is not relatively orientable and new ideas are needed to produce enriched counts. We introduce a fixed "line at infinity," which leads to enriched counts of bitangents that depend on their geometry relative to the quartic and this distinguished line.