Intersection cohomology of hypersurfaces [Elektronische Ressource] / von Lorenz Wotzlaw

Wotzlaw Lorenz

Description

TolfgangChristophtersectionKurkCHumohomologyhaftlicofDr.HypStratenersurfaces18.DISSERzuTanAI:TIONhzurProf.ErlangungDr.desam:akünademiscthenoldt-UnivGradesProf.dohiesctMathematiscorFrerumDr.naturaliumy(Dr.1.rer.Dimcanat.)Herbim3.FvachhJuliMathderehenm2007atikdereingereicbhersitättBerlin:anDr.derMarkscMathematiscDekh-Naturwissenscderhaftlich-NaturwissenschenhenFakultätakProf.uWltätCoIGutacHumter:bProf.oldt-UnivAlexandruersität2.zuDr.BerlinertveonProf.HerrDucoDipl.-Math.anLorenzeingereicWtotzla25.w2006gebagorenmamdlic26.08.1968Prüfung:inMaiKasselInPräsidenFürFundCatrin,ynnAntonfactThentrovidesductionexplicitlyOnisaCG80smostructureoth,hsameyphallenging.ersurfaceanishingIncohomology:inThetseningredienexiste4ishingneedso,.inmaktersectioncohomocohomolothegydtiallyvessen-vGrithsass,ClemensstructuremdgetoHoconcerningtheseesoftodescriptionvexplicitforaneevgivmiddleotTthis.

Sujets

• Mathematics

Informations

• Publié par: humboldt-universitat_zu_berlin
• Publié le: 01 janvier 2007
• Nombre de lectures: 30
• Langue: English

Extrait

agInCotersectionMarkscCeohomologybofhenHypAlexandruersurfaceseingereicDISSERMaiTBerlin:AderTIONProf.zurter:ErlangungDr.desDucoak25.ademiscdlichenderGradesersit?tdoDr.ctDekorh-Naturwissenscrerumakult?tnaturaliumW(Dr.Gutacrer.Prof.nat.)2.imertFProf.acanhtMath2006emmPr?fung:atikteingereicHumholdt-UnivtzuanProf.derChristophMathematischiesh-NaturwissenscanhaftlicMathematischenhaftlicFFakI:uDr.lt?tolfgangIyHumhb1.oldt-UnivDr.ersit?tDimcazuProf.BerlinHerbvKurkon3.HerrDr.Dipl.-Math.vLorenzStratenWhotzlaam:wJuligebTorenderam?n26.08.1968henin18.Kassel2007Pr?sidenundF?rynnCatrin,FAntonnX P =:Y
k kIH (X,C) :=H (X,IC (C)[−n+1])X
C = IC (C)[−n+1].X
n−1(X) X0
k n p(P ,Ω (l)) = 0; k,l≥ 0
• • •0→ Ω → Ω (logX)→ Ω [−1]→ 0Y Y X
k−2 • k •
H (X,Ω )(−1)→ H (Y,Ω )X Y
k • k−1 •
H (Y,Ω (logX))’H (X,Ω )(−1)Y 0 X
k
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X
p • p p+1 nΩ (∗X) :=(Ω (X)→ Ω (2X)→...→ Ω ((n−p+1)X))[−p],
p 0 p 1 p n=( (Ω (∗X)→ (Ω (∗X))→...→ (Ω (∗X)));
p j j(Ω (∗X)) := Ω (1+j−p) j−p≤ 0
•Ω (∗X) log X
• • •0−−−→ Ω −−−→ Ω (logX) −−−→ Ω [−1] −−−→ 0Y Y X
  
  
y y y
0• • • •0−−−→ Ω −−−→ Ω (∗X)−−−→ Ω (∗X)/Ω −−−→ 0Y Y Y Y
r
pq q r p p+q r •= (Y, Ω (∗X)) =⇒ H (Y, Ω (∗X))1
k r • k r •
H (Y, Ω (∗X)) = (Γ(Y, Ω (∗X)),Γ(d))
r Γ(d)
n r • r n r n−1
H (Y, Ω (∗X)) = Γ(Y, Ω (∗X))/dΓ(Y, Ω (∗X)).
n+1 nY :=C −{0} q : Y→P :=Y
P
Y E := x∂ Yi i
p −1Ω (∗ X) X :=q (X) qY
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n
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J := (F ),+ i
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n−p+1F
BΩ n−p+1 nβ = ∈ Γ(Y, (Ω (∗X)[n])
pF
p−1 n−1 n−p n−1(X) (X)0 0
n−p(−1) p! ABΩ n niα∪β = ∈ (J,Ω ),!
n−p! F ·...·F0 n
n−1 n−1 n n ni : (Ω )→ (P ,Ω )! X
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↓ ↓
S = S
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12 ∂S∼ Spec(k[]/hi θ = ks( )∈ (X,Θ )X∂
0 nX → S T ∈ (P ,O(deg(X))) θ
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n−p+2F F
−1Gr (−∪θ) T/F Gr
i)−iv)
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↓ ↓
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ks : Θ → π ΘS ∗ X|S
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n−1S (Θ ) Θ Gr HS S
Gr H S
n−1 nS Θ ⊗π Ω →OS ∗ S
(X ·...·X )⊗ω→hksX ∪...∪ksX ∪ωi ,1 n−1 1 p
4X P
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k k(X,C ) = (Y,i C )X ∗ X
∗i C [n− 1] = i i C [n− 1]∗ X ∗ Y
Y D :
A→ RHom(A,C [2n])Y
A
k −k 2n(Y,A)× (Y,D(A))→ (Y,C)∼C
A A D(A)
∗A = i i (C )∗ Y
∗c X Y i i (C )X|Y ∗ Y
∗ !
D(i i C [n−1]) =i iC [n+1]∗ Y ∗ Y
Γ (C [n+1]YX
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
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0 0 0∗ !(Y,i i C [n−1])× (Y,i iC [n+1])−−−→ (Y,C [2n])∗ Y ∗ Y Y
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C [n−1] ICX X
i IC∗ X
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0 • •eA A := Ω (∗X)/Ω
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•(Ω (∗X)) :=m Y •τ (Ω (∗X)) ; m = 1≤n−1 Y

•Ω (∗X) ; m≥ 2 ,Y
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