Infinitesimal variations of hodge structure (I)
Infinitesimal variations of hodge structure (I)
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Hodge结构的无穷小变化(I)
DOI：
10.1007/bf01175050
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发表时间：
1983
影响因子：
1.8
通讯作者：
J. Harris
中科院分区：
文献类型：
--
作者：
J. Carlson;M. Green;P. Griffiths;J. Harris
商业给人的印象是一种结构性的违规行为。吹捧拷贝你的印象和图片人做的事情，请注意版权。一条光滑的代数曲线C的Hodge结构由它的雅可比簇J(C)和由hl(C，Z)上的交式Q确定的主极化组成。众所周知，这等价于给出对(J(C)，8)，其中8c J(C)是到平移的唯一确定的除数，其基本类在单位H2(J(C)，Z)下是Q的性质；：Hom(A2Hl(C，Z)，Z)。极化Hodge结构(J(C)，O)从椭圆积分的求逆开始，一直延续到目前的研究，在代数曲线理论中起着至关重要的作用。作为标志，我们提到了Abel定理、Jacobi逆定理、Riemann定理、Riemann奇点定理、Andreotti-Mayer定理，以及雅可比变换在特殊因子研究中的应用(参见。[2]和[20]，以精确描述这些结果)。总而言之，人们可能会说，除了人们期望在研究代数曲线时使用的直接几何论点之外，霍奇理论还提供了一种额外的意想不到的和深入的技术。曲线上的阿贝尔积分理论由Picard、Poincaré和Lefschetz等人部分地扩展到更高的维度(参见。[41]，[32])。这一发展在20世纪30年代霍奇的工作中达到顶峰，S(参看。[27])，并构成了现在所说的光滑射影簇的经典霍奇理论。近年来，经典的Hodge理论已经扩展到一般的代数变体(混合Hodge理论；[10]，[17])和代数族(Hodge结构的变种，参见[16]、[9])。这两个扩展相互作用，精确地描述了一个变种在获得奇点时的Hodge结构的极限行为(参见。[44]，[46])。110目前，人们可能会觉得霍奇理论及其扩展构成了一个形式对称性和一定深度的主题(参见。最近的论文[6]、[8]和[50])。鉴于此，我们有理由期待霍奇理论在代数几何中的应用，至少在某种程度上可以与曲线的应用相媲美。但不幸的是，情况还不是这样。当然，经典的霍奇理论有其众所周知的应用(Lefschetz(1，1)定理、霍奇指数定理等)，以及…
tion commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit conte-nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques The Hodge structure of a smooth algebraic curve C consists of its Jacobian variety J(C) together with the principal polarization determined by the intersection form Q on Hl(C, Z). It is well known that this is equivalent to giving the pair (J(C), 8), where 8 c J(C) is a divisor uniquely determined up to translation by the property that its fundamental class be Q under the identification H2(J(C), Z);: Hom(A2Hl (C, Z), Z). Beginning with the inversion of the elliptic integral and continuing through current research, the polarized Hodge structure (J(C), O) has played an essential role in the theory of algebraic curves. As signposts we mention Abel's theorem, the Jacobi inversion theorem, Riemann's theorem, the Riemann singularity theorem, the Andreotti-Mayer theorem, and the use of the Jacobian variety in the study of special divisors (cf. [2] and [20] for precise statements of these results). In sum, one might say that in addition to the direct geometric arguments that one expects to use in studying algebraic curves, Hodge theory provides an additional unexpected and penetrating technique. The theory of abelian integrals on curves was partially extended to higher dimensions by Picard, Poincaré, and Lefschetz, among others (cf. [41], [32]). This development culminated in the work of Hodge in the 1930's (cf. [27]), and constitutes what is now called classical Hodge theory for a smooth projective variety. In recent years classical Hodge theory has been extended to general algebraic varieties (mixed Hodge theory; cf. [10], [17]) and to families of algebraic varieties (variations of Hodge structure, cf. [ 16], [9]). These two extensions interact in the precise description of the limiting behaviour of the Hodge structure of a variety as it acquires singularities (cf. [44], [46]). 110 At present one may feel that Hodge theory and its extensions constitutes a subject of formal symmetry and some depth (cf. the recent papers [6], [8], and [50]). Given this it is reasonable to expect that Hodge theory should have applications to algebraic geometry at least somewhat comparable to what happens for curves. But unfortunately this is not yet the case. Certainly classical Hodge theory has its well known applications (Lefschetz (1,1) theorem, Hodge index theorem, etc.), and …
孤立超曲面奇点的单峰性 I、II
DOI：
--
发表时间：
2009
期刊：
影响因子：
--
作者：
原岡喜重;加藤満生;S. Tanabe,;S. Tanabe
通讯作者：
S. Tanabe