On the embedded Nash problem
Nero Budur, Javier de la Bodega, Eduardo de Lorenzo Poza, Javier, Fern\'andez de Bobadilla, Tomasz Pe{\l}ka
TL;DR
This paper investigates the embedded Nash problem for hypersurfaces, characterizing families of arcs with fixed contact order, and provides solutions for unibranch plane curve germs using resolution graphs.
Contribution
It introduces a geometric characterization of arc families via divisors on minimal models and solves the problem for unibranch plane curve germs.
Findings
Divisors on minimal models contribute to arc families.
Solved the embedded Nash problem for unibranch plane curve germs.
Connected the problem to resolution graphs.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Advanced Differential Equations and Dynamical Systems