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Generalizations of two-dimensional c...

Zhao, Wenhua.

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Generalizations of two-dimensional conformal field theory; some results on Jacobians and intersection numbers.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Generalizations of two-dimensional conformal field theory; some results on Jacobians and intersection numbers./
作者:	Zhao, Wenhua.
面頁冊數:	156 p.
附註:	Source: Dissertation Abstracts International, Volume: 61-03, Section: B, page: 1446.
Contained By:	Dissertation Abstracts International61-03B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9965182
ISBN:	0599696958

Generalizations of two-dimensional conformal field theory; some results on Jacobians and intersection numbers.
Zhao, Wenhua.

Generalizations of two-dimensional conformal field theory; some results on Jacobians and intersection numbers. - 156 p.

Source: Dissertation Abstracts International, Volume: 61-03, Section: B, page: 1446.

Thesis (Ph.D.)--The University of Chicago, 2000.

My dissertation consists of three different topics. In the first topic, I consider the generalizations of two dimensional genus zero or tree level conformal field theory to the setting of locally trivialized holomorphic vector bundles and principal GC -bundles over the Riemann sphere, where G is any connected and simply connected semi-simple Lie group G and GC is the complexification of G. With the sewing operations of bundles and the permutations of symmetric groups on the local trivializations, the moduli spaces of locally trivialized holomorphic vector bundles and principal GC -bundles over the Riemann sphere form analytic partial operads. First, we study the holomorphic operadic structure on the moduli spaces of locally trivialized holomorphic vector bundles and principal GC -bundles over the Riemann sphere and their relations with the loop groups, the group Dif f+(S 1) as well as the infinite dimensional Grassmannians. Secondly, we classify and construct explicitly all 1-dimensional modular functors over the moduli spaces of locally trivialized holomorphic vector bundles and principal GC -bundles over the Riemann sphere, including the determinant line bundles. Thirdly, we show that the category of the meromorphic algebras of 1-dimensional modular functor E&d15;G C is isomorphic to the category of what we call the integrable generalized affine vertex operator algebras.

ISBN: 0599696958Subjects--Topical Terms:

515831
Mathematics.

Generalizations of two-dimensional conformal field theory; some results on Jacobians and intersection numbers.
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245 1 0 $a Generalizations of two-dimensional conformal field theory; some results on Jacobians and intersection numbers.
300 $a 156 p.
500 $a Source: Dissertation Abstracts International, Volume: 61-03, Section: B, page: 1446.
500 $a Adviser: Spencer Bloch.
502 $a Thesis (Ph.D.)--The University of Chicago, 2000.
520 $a My dissertation consists of three different topics. In the first topic, I consider the generalizations of two dimensional genus zero or tree level conformal field theory to the setting of locally trivialized holomorphic vector bundles and principal GC -bundles over the Riemann sphere, where G is any connected and simply connected semi-simple Lie group G and GC is the complexification of G. With the sewing operations of bundles and the permutations of symmetric groups on the local trivializations, the moduli spaces of locally trivialized holomorphic vector bundles and principal GC -bundles over the Riemann sphere form analytic partial operads. First, we study the holomorphic operadic structure on the moduli spaces of locally trivialized holomorphic vector bundles and principal GC -bundles over the Riemann sphere and their relations with the loop groups, the group Dif f+(S 1) as well as the infinite dimensional Grassmannians. Secondly, we classify and construct explicitly all 1-dimensional modular functors over the moduli spaces of locally trivialized holomorphic vector bundles and principal GC -bundles over the Riemann sphere, including the determinant line bundles. Thirdly, we show that the category of the meromorphic algebras of 1-dimensional modular functor E&d15;G C is isomorphic to the category of what we call the integrable generalized affine vertex operator algebras.
520 $a In the second topic, by using the theory of Residues and Intersection Numbers in complex algebraic geometry, I study some algebraic relations between the Jacobians and the intersection numbers for the affine curves in C2 . I also consider some relations between the results I get and the well known Jacobian Conjecture.
520 $a In the third topic, I first prove an exponential formula for the Jacobians of analytic maps. Then I consider some consequences of this formula, especially its relations with Jacobian Conjecture.
590 $a School code: 0330.
650 4 $a Mathematics. $3 515831
650 4 $a Physics, Elementary Particles and High Energy. $3 1019488
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710 2 0 $a The University of Chicago. $3 1017389
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790 1 0 $a Bloch, Spencer, $e advisor
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