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ࢯ໊ɿߴࢁໜ
໊ɿෳૉղੳɾෳૉزԿ,زԿ
Ωʔϫʔυɿෳૉଟ༷ମ,K¨ahlerଟ༷ମ,ඪ४ଋ,ଟ༷ମͷۃখϞσϧཧ,খ
ฏܕফ໓ఆཧ,L2-ධՁࣜ,∂-ํఔࣜ
ݱࡏͷݚڀ֓ཁɿ
ɹෳૉଟ༷ମΛෳૉزԿతͳํ๏ʹΑΓݚڀ͍ͯ͠Δɻಛʹʮඪ४ଋͷෳૉزԿֶʯ
ͱ͍͏ςʔϚͰݚڀΛߦ͍ͬͯΔɻෳૉଟ༷ମͷඪ४ଋͱKX=∧nT!ʢT!Xͷਖ਼
X X
ଇଋͷରʣͷ͜ͱͰ͋Δɻෳૉଟ༷ମͷʮزԿʯΛௐΑ͏ͱ͢Δͱ͖ʹɺͦͷ্ʹ
ଘࡏ͍ͯ͠Δղੳతରʢਖ਼ଇؔɺ༗ཧܕؔɺඍܗࣜͳͲʣͷಛΛௐΔ͜ͱͰ
ཧղ͢Δɺͱ͍͏ݚڀͷํ͕͋Δɻ͞Βʹͦͷղੳతରͷද֨ͱͯ͠ඪ४ଋͷۊ
K"mͷਖ਼ଇஅΛ༻͍Δ͜ͱ͕͋͠͠Δɻ͜Ε͕ඪ४ଋͷඪ४ͨΔॴҎͰ͋Δɻඪ
X
ޠతʹʮඪ४ଋͯ͢ΛޠΔʯͱݴ͑Δɻ͜ͷߟ͑ͷڀۃͷҰྫ͕ଟ༷ମͷۃখ
ϞσϧཧͰ͋Δɻඪ४ଋͷۊͷஅΛߏ͢Δͱ͖ʹɺ∂-ํఔࣜʢίʔγʔɾϦʔϚ
ϯํఔࣜʣͷՄղੑɺਖ਼ଇؔͷL2֦ுఆཧͳͲͷղੳతख๏Λ༻͍Δɻଞํɺέʔ
ϥʔɾΞΠϯγϡλΠϯܭྔʹද͞ΕΔඪ४έʔϥʔܭྔͷزԿֶɺϞϯδϡ-Ξϯ
ϖʔϧํఔࣜʹද͞ΕΔඇઢܗภඍํఔࣜͷՄղੑʹؼண͞ΕΔɻඪ४έʔϥʔܭྔ
ͷଘࡏɺଟ༷ମͷ҆ఆੑɺϞδϡϥΠཧͱີʹ͍ؔͯ͠ΔʢϠ-ςΟϠϯ-υ
φϧυιϯ༧ʣɻزԿʹ͓͚ΔεΩʔϜͷΑ͏ͳۭؒͷಛҟࣗ༝ʹѻ͑Δ
తΈɺ௨ৗͷղੳزԿͷखͷಧ͔ͳ͍෦Λཧղ͢Δ্ͰෆՄܽͰ͋Δɻ͜ͷ
Α͏ʹɺزԿɺղੳ͔͍ͪؔʹ͋Δɻʢෳૉղੳࣗମͷݚڀ͍ͯ͠ͳ͍ɻʣ
ֶੜͷཁɿ
ͷجૅɺଟ༷ମɺҰมؔ͢Ͱʹशಘ͍ͯ͠Δͷͱͯ͠ɺͦΕΛجૅ
ͱͯ͠زԿɺඍزԿɺଟมؔɺͱίϗϞϩδʔͳͲΛษڧͯ͠΄͍͠ɻ
ɺزԿɺղੳ͕ަࠩ͢Δݚڀʹڵຯͷ͋ΔֶੜΛܴ͢Δɻؔ͢Δຊͱͯ࣍͠ͷ
ͷ͕ڍ͛ΒΕΔɻଠࣈͷͷ֘ͷදతͳೖॻͷҰͭɻ
زԿ:
ɹHartshorne: Algebraic geometry, Springer GTM 52, ༁͋Γ.
ɹLazarsfeld: Positivity in algebraic geometry I, II, Springer.
ෳૉزԿ:
ɹখฏ: ෳૉଟ༷ମ.
ɹখྛতࣣ: ෳૉزԿ1,2,ؠ.
ɹHuybrechts: Complex Geometry, Springer.
ɹWells: Di!erential analysis on complex manifolds, Springer GTM 65.
ɹDemailly: Analytic methods in algebraic geometry, International Press.
ɹGri!ths-Harris: Principles of algebraic geometry.
ଟมؔ:
ɹH¨ormander: Complex analysis in several variables, ༁͋Γ.
ɹେ݈: ଟมෳૉղੳ,ؠ.
ɹதໜஉ: ଟมവ–ඍزԿֶతΞϓϩʔν–,ேॻళ.
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