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SUMMARY:Pseudolattices\, del Pezzo surfaces\, and fibrations over discs. -
  Alan Thompson\, Cambridge
DTSTART:20180530T131500Z
DTEND:20180530T141500Z
UID:TALK106099@talks.cam.ac.uk
CONTACT:Mark Gross
DESCRIPTION:The theory of pseudolattices was initiated by Kuznetsov\,\nbui
 lding on work of many other authors. The canonical example is the\nnumeric
 al Grothendieck group associated to the bounded derived category\nof coher
 ent sheaves on a smooth variety. In this talk I will introduce a\nspecial 
 class of pseudolattices\, which may be thought of as numerical\nGrothendie
 ck groups associated to bounded derived categories of coherent\nsheaves on
  smooth rational surfaces which admit a smooth anticanonical\ndivisor. Suc
 h pseudolattices may be classified and\, perhaps\nunsurprisingly\, their c
 lassification parallels the well-known\nclassification of del Pezzo surfac
 es.\n\nHowever\, this special class of pseudolattices also arises naturall
 y in a\nsecond context\, associated to a certain class of elliptic Lefsche
 tz\nfibrations over complex discs. I will show that the classification\nre
 sult above allows one to classify such elliptic Lefschetz fibrations\nup t
 o symplectomorphism. This setting should be thought of as mirror\, in\na h
 omological sense\, to the original context of smooth rational surfaces\nad
 mitting smooth anticanonical divisors. This work is joint with Andrew\nHar
 der.
LOCATION:CMS MR13
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