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Asymptotics of Fubini-Study Currents...

Wolff, Melody A.,

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Asymptotics of Fubini-Study Currents for Sequences of Line Bundles /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Asymptotics of Fubini-Study Currents for Sequences of Line Bundles // Melody A Wolff.
作者:	Wolff, Melody A.,
面頁冊數:	1 electronic resource (84 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31939609
ISBN:	9798280793637

Asymptotics of Fubini-Study Currents for Sequences of Line Bundles /
Wolff, Melody A.,

Asymptotics of Fubini-Study Currents for Sequences of Line Bundles /Melody A Wolff. - 1 electronic resource (84 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

Let (X,ω) be a Kahler manifold, and Lp be a sequence of line bundles on X equipped with continuous hermitian metrics hp Let γp be the Fubini-Study current and hpeq the equilibrium metric corresponding to the metric hp Our goal is to generalize a theorem of Tian in Complex Geometry to a setting using arbitrary line bundles equipped with metrics with non-positive curvature. This amounts to finding sufficient conditions for γp − c1(Lp, hpeq) when appropriately scaled, to converge to 0 in the sense of currents. To achieve this goal, we imply methods of Demailly and the Oshawa-Takegoshi Extension Theorem to bound a scaled potential for γp - c1(Lp, hpeq) and show that it converges in L1.After we establish sufficient conditions for the aforementioned convergence, we ask the question of when do γp and c1(Lp, hpeq) converge. To simplify our investigation, we restrict ourselves to the case where c1(Lp, hp) converges. We establish sufficient conditions for the convergences of γp using methods similar to our previous results. In this case, a construction of the limit is given, which is defined as a particular upper quasi-plurisubharmonic envelope.Lastly, we establish application of our results to special cases. In particular, we discuss the cases where (Lp, hp) is a tensor product of powers of line bundles, that is (Lp, hp) is of the form (F1⊗m1,p ⊗⋯⊗ Fk⊗m k,p , h1⊗m1,p ⊗⋯⊗ hk⊗mk,p) for some metrics (Fj, hj) and mj,p ∈ ℕ. This particular case is handled using the fact that the weights of h1⊗m1,p ⊗⋯⊗ hk⊗mk,p are a sum of the weights of the metrics h1 ,...,hk .

English

ISBN: 9798280793637Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Analysis

Asymptotics of Fubini-Study Currents for Sequences of Line Bundles /
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520 $a Let (X,ω) be a Kahler manifold, and Lp be a sequence of line bundles on X equipped with continuous hermitian metrics hp Let γp be the Fubini-Study current and hpeq the equilibrium metric corresponding to the metric hp Our goal is to generalize a theorem of Tian in Complex Geometry to a setting using arbitrary line bundles equipped with metrics with non-positive curvature. This amounts to finding sufficient conditions for γp − c1(Lp, hpeq) when appropriately scaled, to converge to 0 in the sense of currents. To achieve this goal, we imply methods of Demailly and the Oshawa-Takegoshi Extension Theorem to bound a scaled potential for γp - c1(Lp, hpeq) and show that it converges in L1.After we establish sufficient conditions for the aforementioned convergence, we ask the question of when do γp and c1(Lp, hpeq) converge. To simplify our investigation, we restrict ourselves to the case where c1(Lp, hp) converges. We establish sufficient conditions for the convergences of γp using methods similar to our previous results. In this case, a construction of the limit is given, which is defined as a particular upper quasi-plurisubharmonic envelope.Lastly, we establish application of our results to special cases. In particular, we discuss the cases where (Lp, hp) is a tensor product of powers of line bundles, that is (Lp, hp) is of the form (F1⊗m1,p ⊗⋯⊗ Fk⊗m k,p , h1⊗m1,p ⊗⋯⊗ hk⊗mk,p) for some metrics (Fj, hj) and mj,p ∈ ℕ. This particular case is handled using the fact that the weights of h1⊗m1,p ⊗⋯⊗ hk⊗mk,p are a sum of the weights of the metrics h1 ,...,hk .
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650 4 $a Theoretical mathematics. $3 3173530
653 $a Analysis
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653 $a Complex geometry
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653 $a Pluripotential theory
653 $a Several complex variables
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