Geodesic
On the embedded Nash problem
Forum of Mathematics, Pi, Tome 12 (2024)

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The embedded Nash problem for a hypersurface in a smooth algebraic variety is to characterize geometrically the maximal irreducible families of arcs with fixed order of contact along the hypersurface. We show that divisors on minimal models of the pair contribute with such families. We solve the problem for unibranch plane curve germs, in terms of the resolution graph. These are embedded analogs of known results for the classical Nash problem on singular varieties. 
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Nero Budur; Javier de la Bodega; Eduardo de Lorenzo Poza; Javier Fernández de Bobadilla; Tomasz Pełka. On the embedded Nash problem. Forum of Mathematics, Pi, Tome 12 (2024). doi: 10.1017/fmp.2024.13

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