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研究生:郭子昂
研究生(外文):Tzu-Ang Kuo
論文名稱:Landau-Ginzburg模型的形變參數空間所聯繫的Frobenius流形
論文名稱(外文):Frobenius Manifolds Associated to the Deformation Parameter Space of Landau-Ginzburg Models
指導教授:余正道
指導教授(外文):Jeng-Daw Yu
口試委員:王金龍李元斌
口試委員(外文):Chin-Lung WangYuan-Pin Lee
口試日期:2018-07-26
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:英文
論文頁數:22
中文關鍵詞:Laudau-Ginzburg模型Frobenius流形環面多樣體平滑Fano多胞形
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  • 收藏至我的研究室書目清單書目收藏:0
首先,我們證明Landau-Ginzburg模型。接著,在數個假設之下,我們證明在Landau-Ginzburg模型的泛形變參數空間上能連繫出一個沒有度量與Euler場的Frobinus流形。對於那些支撐集是平滑Fano多胞形的非退化Laurent多項式,我們證明這些假設為真。
We first prove the Local Torelli Theorem for Landau-Ginzburg models. Next, under several conditions, we prove that there is a Frobenius manifold without metric and Euler field, associated to the universal parameter space of Landau-Ginzburg models. We prove these assumptions hold true for every nondegenerate Laurent polynomial whose support polytope is a smooth.
口試委員會審定書…………………………………………………………………. #
誌謝…………………………………………………………………………………...i
中文摘要……………………………………………………………………………..ii
ABSTRACT………………………………………………………………………….iii
CONTENTS………………………………………………………………………….iv
Chapter 0 Introduction…………….………………………………………………….1
Chapter 1 Local Torelli Theorem…………………………………………………….3
Chapter 2 Frobenius manifold without metric and Euler field……………………….8
2. 1 The construction theorem……………………………………………………8
2.2 Discussion for Laudau-Ginzburg models………………………………….10
Chapter 3 Construction in Toric Case……………………………………………….16
References………………………………………………………………………...…21
[ESY17] Hélène Esnault, Claude Sabbah, and Jeng-Daw Yu. E1-Degeneration of the Irregular Hodge
Filtration (with an Appendix by Morihiko Saito). Journal für die reine und angewandte Mathematik,
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[FIM] Domenico Fiorenza, Donatella Iacono, and Elena Martinengo. Differential Graded Lie Algebras
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Princeton University Press, 1993.
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of Japan, 26(4):647–67, 1974.
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Inventiones mathematicae, 18:1–118, 1972.
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[KO68] Nicholas Katz and Tadao Oda. On the Differentiation of De Rham Cohomology Classes with
respect to Parameters. Journal of Mathematics of Kyoto University, 8(2):199–213, 1968.
[Man] Marco Manetti. Deformation Theory via Differential Graded Lie Algebras.
[Nil05] Benjamin Nill. Gorenstein Toric Fano Varieties. manuscripta mathematica, 116(2):183–210,
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[Sab06] Claude Sabbah. Hypergeometric Periods for a Tame Polynomial. 63(2), 2006.
[Ser06] Edoardo Sernesi. Deformations of Algebraic Schemes, volume 334 of Grundlehren der mathematischen
Wissenschaften. Springer-Verlag Berlin Heidelberg, 2006.
[SY15] Claude Sabbah and Jeng-Daw Yu. On the irregular Hodge filtration of exponentially twisted
mixed Hodge modules. 3, 2015.
[Voi08] Claire Voisin. Hodge Theory and Complex Algebraic Geometry I. Cambridge University Press,
2008.
[Yu14] Jeng-Daw Yu. Irregular Hodge Filtration on Twisted De Rham Cohomology. Manuscripta
Mathematica, 144(1):99–133, 2014.
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