Singularity invariants based on arcs and the Nash multiplicity sequence

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Date(s) - 14/02/2019
14 h 00 min - 15 h 00 min

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Arc spaces are useful in the study of singularities, since they detect certain properties of algebraic varieties, including smoothness. They also let us define numerous invariants. In particular, the Nash multiplicity sequence, defined by M. Lejeune-Jalabert for germs of hypersurfaces and generalized later by M. Hickel, is a non-increasing sequence of positive integers attached to an arc in the variety which stratifies the arc space in a similar way in which the multiplicity function stratifies the variety.

In this talk, we will define this sequence and we will show how it gives rise to a series of invariants of singularities. They turn out to be strongly related to those that we use for constructive resolution of singularities for varieties defined over fields of characteristic zero.
We will also explain some results in this direction.

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