Global HMS for Genus Two · 2020. 11. 6. · Genus two complex curve I I C Muz E symmetric Im I o...

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Global HMS for Genus Two Curves with Haniya Azam Catherine Cannizzo Chiu Chu Melissa Liu Torus Polishchuk Easton 1998 E I ez 1 2 112 2 WE Idrrdo I Bt is C Upper half plane r o Dblcohlee Fuk T wa Ll txt picture from Auemestatks lo s eo I a Area LI e Lo 57 L E Ei.e2iiSw o e

Transcript of Global HMS for Genus Two · 2020. 11. 6. · Genus two complex curve I I C Muz E symmetric Im I o...

  • Global HMS for Genus Two Curveswith Haniya Azam CatherineCannizzo Chiu ChuMelissaLiu

    Torus Polishchuk Easton 1998

    E I ez 12 112 2 WE Idrrdo

    I Bt is C Upper half plane r o

    Dblcohlee Fuk T wa

    Ll txtpicture fromAuemestatks lo s eo

    I aArea LI eLo 57 L E

    Ei.e2iiSwo

    e

  • L XERIZ LxLo si e si Eo

    an n

    e Ade AreaArea 2THI sZ

    j eo si Eo

    k k ke e

    Lo 57 L E xp

    I e2iid eoNEE

    OS L EV Gtx

    TX E ne.Itzein2 L 2 inx L

    etiXZnq.ge

    aiTlnzX2degj

    line bundles t Lagrangian slope jskyscraper sheaf Vertical Lagrangian

  • Genus two complex curve

    I I C Muz E symmetric Im I o

    OH x it x thx noneThink

    o

    n th nzC212M

    V 2,2 lXiiX27E FYxnxdnELm.cxi.x

    A Tn Nlt TIZNz

    x e2aivT FL XD Iz n Izz ha

    X1 K2

    e2TiV Ii Innit 42M e2Tif2lMtT22n

    Vet z ezz vi b EE z2t 22

    E T 4 torus

    SYZ Mirror symmetry Abouzaid Auroux Katzarkou 2012

    Replace e by XEB qg Vex E

  • generic Singular AzYa fiber fiber A's q

    VY T4 P43m I Ask

    symplecticvo

    fibration

    way

    of

    10

    Crit Vo GUGU GETCj CR with symplectic area Aj

    HMS

    it L LIohhh Cohl e

    Fukayaf Cannizzo

    2002 2019

    v v

    Fukf.VEU

    s ESTE v