Intensive Course on the Nash problem of arcs |
Lecturer: Ana Reguera (University of
Valladolid)
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What is the Nash problem of
arcs?
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In a 1968 preprint, later published
as [Arc structure of singularities, Jr. Duke Math. J. 81, A celebration of
John F. Nash] , Nash initiated the use of arcs in the study of singularities
of algebraic and analytic varieties. An arc can thought to be an infitesimal
curve on the variety. By the celebrated theorem of Hironaka
a variety over the complex numbers has a resolution
of singularities: there is a morphism from a non-singular variety which
is an isomorphism outside the singular locus, whereas singularities give
raise to a finite number of codimension one subvarieties of the non-singular
variety. The latter are called the exceptional divisors. Nash proved that
arcs through singularities decompose into a finite number of families, and
that these families correspond injectively to those exceptional divisors
which appear on every resolution. He asked if the converse also holds: Does
every such exceptional divisor correspond to an arc family?
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Wednesday 26.10.
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14-16 |
B321
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Introduction to the space of arcs I
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| Thursday 27.10. |
10-12
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B321
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Introduction to the space of arcs II
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Friday 28.10
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10-12
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B321
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The Nash problem of arcs and the wedge
problem
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Monday 31.10.
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C129 |
10-12
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A new finiteness property on the space
of arcs: A Curve Selection Lemma
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