Abstract:We study contact loci sets of arcs and the behavior of Hironaka's order function defined in constructive Resolution of singularities. We show that this function can be read in terms of the irreducible components of the contact loci sets at a singular point of an algebraic variety.
ContentsIntroduction 1 1. Arcs, valuations and contac loci 5 2. Nash multiplicity sequences, the persistance, and the Q-persistance 8 3. Rees algebras 11 4. Local presentations of the Multiplicity 13 5. Hironaka's order function, the… Show more
“…A consequence of Theorem 1.1 is that ord (d) X (ξ) can be defined without using étale topology and only studying properties of its space of arcs. Moreover the arc η realizing the minimum in (1.1.2) can be choosen, and constructed explicitly, being fat and divisorial [9,Theorem 6.3]. In other words, the refinement of the multiplicity for the resolution function in (1.0.4) can be obtained by studying sequences of Nash multipicities sequences in L(X).…”
Section: Nash Multiplicity Sequences and Constructive Resolutionmentioning
We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varieties.
“…A consequence of Theorem 1.1 is that ord (d) X (ξ) can be defined without using étale topology and only studying properties of its space of arcs. Moreover the arc η realizing the minimum in (1.1.2) can be choosen, and constructed explicitly, being fat and divisorial [9,Theorem 6.3]. In other words, the refinement of the multiplicity for the resolution function in (1.0.4) can be obtained by studying sequences of Nash multipicities sequences in L(X).…”
Section: Nash Multiplicity Sequences and Constructive Resolutionmentioning
We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varieties.
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