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UID:2801@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190314T140000
DTEND;TZID=Europe/Paris:20190314T150000
DTSTAMP:20190227T130000Z
URL:https://www.i2m.univ-amu.fr/evenements/ultrametric-properties-for-valu
 ation-spaces-of-normal-surface-singularities/
SUMMARY: (...): Ultrametric properties for valuation spaces of normal surfa
 ce singularities
DESCRIPTION:: Let (X\,x_0) be a normal surface singularity\, and denote by 
 B_X the set of irreducible curves (branches) at (X\,x_0).Consider the func
 tional u_L(A\,B)=(L · A) (L · B) / (A · B)\, where L\,A\,B are branches
 .In a joint work with E. García Barroso\, P. González Pérez and P. Pope
 scu Pampu\, we show that u_L defines an (extended) ultrametric distance on
  B_X for a (any) branch L if and only if (X\,x_0) is arborescent: the dual
  graph of any good resolution is a tree.The proof relies on intersection p
 roperties of exceptional divisors\, obtained in collaboration with W. Gign
 ac.I will present this result\, and an analogous statement on the space V_
 X of (rank-1 normalized semi-)valuations at (X\,x_0).If time allows\, I wi
 ll also present a topological condition on dual graphs (resp.\, valuation 
 spaces) to ensure that u_L is an ultrametric on a given subset of B_X (res
 p.\, V_X).http://webusers.imj-prg.fr/~matteo.ruggiero/
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