Geodesic
A short proof of the multiple cover formula for point insertions
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e200

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A few years ago, G. Oberdieck conjectured a multiple cover formula 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. 
Blomme, Thomas. A short proof of the multiple cover formula for point insertions. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e200. doi: 10.1017/fms.2025.10139
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