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SUMMARY:Numerical and linear equivalence of divisors in birational geometr
 y - Anne-Sophie Kaloghiros (Cambridge)
DTSTART:20110525T131500Z
DTEND:20110525T141500Z
UID:TALK31045@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:Let X be a smooth projective variety and D a divisor on X. The
  MMP is\nconcerned with determining a "good" model for D\n--\nthat is\, a 
 variety X'\nbirational to X on which the image of D is a divisor with good
 \npositivity properties. In this talk\, I will examine which part of this\
 npicture depends on the numerical equivalence class of D (topological\npro
 perties) and which part depends on its linear equivalence class\n(algebro-
 geometric properties).\nI will introduce the numerical Zariski Decompositi
 on of divisors.\nUnder the hypothesis of finite generation\, it can be\nus
 ed to recover Shokurov's polytopes and to describe the relationship\nbetwe
 en different end products of the MMP on klt pairs (X\, D) when D\nvaries.
LOCATION:MR13\, CMS
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