2025/01/02 by Blomme, Thomas
#14K12 #14T90 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14N10 #Secondary 14N35
paper · doi:10.48550/arxiv.2501.01274
A few years ago, G. Oberdieck conjectured a multiple cover fomula that determines the number of curves of fixed genus and degree passing through a configuration of points in an abelian surface. This formula was proved by the author using tropical techniques and Nishinou's correspondence theorem. Using the same techniques, we give a much shorter proof of the multiple cover formula for point insertions, relying on the same geometrical idea, but avoiding any kind of tropical enumeration.