当然对阿贝尔群这个想法至少和霍奇(Hodge)理论一样古老,并且得益于阿提亚(Atiyah),博特(Bott),德里费尔德(Drinfeld),希钦(Hitchin),马宁(Manin),唐纳森(Donaldson),辛普森(Simpson)和威腾(Witten)的工作[3,5,4,18,43,49],非阿贝尔群的情况和物理有越来越多深刻的联系。 但是我的印象是多数数学家并不知道主丛的...
Introduction to nonabelian Hodge theory: flat connections, Higgs bundles and complex variations of Hodge structure. In Calabi-Yau varieties: arithmetic, geometry and physics, vol. 34 of Fields Inst. Monogr. Fields Inst. Res. Math. Sci., Toronto, ON, 2015, pp. 131-171....
Hodge theory and complex algebraic geometry I : vol.1 Voisin, Claire; Bollobás, B; Fulton, W; Katok, A; Kirwan, F; Sarnak, P; Schneps, Leila V Claire,S Leila - 《Cambridge University Press Cambridge》 被引量: 7发表: 2010年 Introduction to Nonabelian Hodge Theory: flat connections, Hi...
An algebraic geometer by training, he has done research at the interface of algebraic geometry,topology, and differential geometry, including Hodge theory, degeneracy loci, moduli spaces of vector bundles, and equivariant cohomology. He is the coauthor with Raoul Bott of "Differential Forms in ...
Spatial diamonds were introduced by Scholze to give geometric structure to naturally arising moduli spaces in p-adic Hodge theory. The theory of diamonds can be thought of as a generalization of the theory of rigid spaces. Scholze further propo...
上面只是粗糙的比喻。实际上为了能计算出正确结果,那个连续区域也要变。变成什么?由Hodge star来计算 。 Hodge star为什么那么定义?论文里有说: We again attempt to motivate the definition with some intuition. When transferring a quantity from a primal simplex to a dual cell, the quantities must “agree...
The purpose of this section is to provide a simple introduction to Clifford algebra, also known as geometric algebra. I assume that you have at least some prior exposure to the idea of vectors and scalars. (You do not need to know anything about matrices.)...
上面只是粗糙的比喻。实际上为了能计算出正确结果,那个连续区域也要变。变成什么?由Hodge star来计算 。 Hodge star为什么那么定义?论文里有说: We again attempt to motivate the definition with some intuition. When transferring a quantity from a primal simplex to a dual cell, the quantities must “agree...
经典的Hodge theory着重讨论紧致 Kaehler 流形的同调群上的Hodge structures,我们通常称之为 pure Hodge structures; 而在代数几何中应用最广泛的是Mixed Hodge structures, 之前的pure Hodge structures只是它的一种特殊情形。我们将简要描述Mixed Hodge structures的定义,基本性质并给出一些应用。
Graduate Texts in Mathematics(共230册), 这套丛书还有 《Graph Theory》《A Course in Commutative Algebra》《Differential Forms in Algebraic Topology (Graduate Texts in Mathematics)》《Theory of Bergman Spaces》《Functional Analysis, Calculus of Variations and Optimal Control》 等。