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Enumerating genus g curves passing through g points in an abelian surface is a natural
problem, whose difficulty highly depends on the degree of the curves. For "primitive"
degrees, we have an easy explicit answer. For "divisible" classes, such a resolution
is quite demanding and often out of reach. Yet, the invariants for divisible classes
easily express in terms of the invariants for primitive classes through the multiple
cover formula, conjectured by G. Oberdieck a few years ago. In this talk, we'll show
how tropical geometry enables to prove the formula without any kind of concrete
enumeration.
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