IV Birational hyperkahler manifolds

Arnaud Beauville

Description

IV. Birational hyperkahler manifolds Arnaud Beauville Universite de Nice March 28, 2008 Arnaud Beauville IV. Birational hyperkahler manifolds

• can blow


• blow up


• birational hyperkahler


• k3 surface


• x0 has


• universite de nice

Sujets

• Beauville
• Blow up
• K3 surface
• Universidad de Niza Sophia Antipolis

Informations

• Publié par: pefav
• Nombre de lectures: 32
• Langue: English

Extrait

ABdaenruaelVIvuliioatir.Beryplhnamrelha¨ksdlofina

IV.

manifolds

Birationalhyperka¨hler

Universit´edeNice

Arnaud Beauville

March 28, 2008

foflysuK3→D:Xmifaohevomtoses,frca X 0 ha oth,XsmorD ∗ ; clacol .sedonenos zy(xesatinrdoo+ 2 y+ P . 2 z bllubkca ts)a(x,fzyx 2 )= 7tt→ / 2 D / aYstx:+ 2 yt7→t 2 : Y //  X  D msY b
Ynicxe,htoo t 22 =+zy 2 pswulo . Bir.cuqda oldw aC b nonaleptisor=divi :nghcaeiluranwognol

manifolds

erk¨ahler

hyp

Birational

IV.

Beauville

Arnaud

Atiyah’s

example

col le 2 +=x+zy 2 Pu 2 . ballybkct→7t / Y : 2 X  / alcoordinates(xy)zta,s(fxy)z ,htoomsY b
Ynispuisivldnaioptceex ta:s // Y D →7 2 t  t D Blow =t 2 . 2 +z 2 x 2 +y duanuaeB nilu rA :g raBiontillviV.eI ciC.na lb roq=aurd ongeachrowdownal sdlofin

X 0 has one nodes.

smooth,

f:X →Dfamily of K3 surfaces, smooth overD

∗ ;X

rkpehyalmaerhl¨a xamph’setiyaA