Studies on moduli spaces from the view point of mathematical physics

从数学物理角度研究模空间

• 批准号: 07304003
• 负责人: UENO Kenji
• 金额: $ 3.65万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07304003/
• 关键词: moduli space; conformal field theory; conformalblock vector bundle; Calabi-Yaumanifold; pointed Riemannsurface; arithmeticgeometry; q-analog; 弦理論; 代数曲線; ベクトル束のモジュライ空間; リーマン面のモジュライ空間; 単純リイ代数; ゲージ対称性; KZ方程式; 閉リーマン面; 共形場ブロック; ベクトル束; 楕円曲面; 変

Moduli spaces of algebraic varieties and vector bundles play am important role not only in algebraic geometry but alsomathematical physics. We studied moduli spaces from the view point of mathematical physics.Ueno studied mainly conformal field theory which has deep relationship with moduli spaces of pointed Riemann surfaces. He showed that non-abelian conformal field theory, so called the WZW modelis defined overtherational number field and even more it can be defined over a discrete valuation ring. With Y.Shimizu and T.Suzuki he also studied explicit description of protectively flat connection of the sheaf of conformal blocks.Maruyama showed a new method how to construct moduli sapce of stable sheaves on algebraic surfaces, which will play an important role to study boundaries of the moduli spaces. Mukai studied the moduli spaces of vector bundles on K3 surfaces and found interesting relationship with the moduli spaces of algebraic curves. Kawamata showed unobstractedness of deformations of Calabi-Yau manifolds by purely algebraic method. Katsura studied pluricanonical sytems of elliptic surfaces in positive characteristics and showed that they have similar properties as in characteristic O.In this way we found many interesting properties of moduli spaces and also showed deep relationship with mathematicalphysics.

代数品种和矢量束的模量空间不仅在代数几何形状，而且在Alsomethemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemathemation中发挥着重要作用。我们从数学物理学的角度研究了模量空间。UENO研究了主要的保形场理论，该理论与尖头的Riemann表面的模量空间有着深厚的关系。他表明，非 - 亚伯共同场理论，所谓的WZW模型定义了过度的数字场，甚至可以在离散的估值环上定义它。借助Y.Shimizu和T.Suzuki，他还研究了对形块捆的保护性平坦连接的明确描述。Maruyama展示了一种新方法，如何在代数表面上构造稳定滑轮的模量，这将在研究模块空间的界限上起重要作用。 Mukai研究了K3表面上向量束的模量空间，并发现了与代数曲线的模量空间有趣的关系。 Kawamata通过纯粹的代数方法表现出卡拉比（Calabi-Yau）歧管变形的未折叠性。 Katsura研究了椭圆表面的元素表面的多元型系统，并表明它们具有与特征性O.的特性相似的特性，我们发现了模量空间的许多有趣的特性，并且还显示了与数学物理学的深层关系。

项目成果

UENO, Kenji: "Q-strurcture of conformal field theory" Progress in Math.129. 511-531 (1995)

UENO，Kenji：“共形场论的 Q 结构”数学进展 129。

桂利行: "Multicanonical system of elliptic surfaces in small characteristic" Compositio Math.97. 119-134 (1995)

Toshiyuki Katsura：“小特征椭圆曲面的多规范系统”Compositio Math.97 (1995)。

上野健爾: "代数幾何入門" 岩波書店, 343 (1995)

Kenji Ueno：《代数几何导论》岩波书店，343（1995）

川又雄二郎: "Unobstracted deformations II" J. Algebraic Geometry. 4. 277-279 (1995)

Yujiro Kawamata：“无阻碍变形 II”J.代数几何。4. 277-279 (1995)

丸山正樹: "Instantons and parabolic sheaves" Proc.Internl.Coloquim on Geometry and Analysis. 245-268 (1995)

Masaki Maruyama：“瞬时和抛物线滑轮”Proc.Internl.Coloquim on Geometry and Analysis 245-268 (1995)。