Helix Theory and Nonsymmetrical Bilinear Forms
Helix Theory and Nonsymmetrical Bilinear Forms
复制标题
螺旋理论和非对称双线性形式
DOI：
10.1007/978-3-322-99342-7_6
复制
发表时间：
1994
期刊：
影响因子：
--
通讯作者：
A. Gorodentsev
中科院分区：
文献类型：
--
作者：
A. Gorodentsev
本文将讨论例外向量丛集的组合结构的描述与单模（非对称）双线性型的一些自然问题之间的联系。为了研究例外向量丛的集合（这样的丛Exti（E，E= 0，对于i ∈ 0和dim Ext0（E，E= 1）），五年前在[GR]，[G1]，[G2]中发展了螺旋理论。在第一节中，我们给出了该理论的主要结果的回顾。在第二节中，我们利用具有非对称非退化整数双线性型的格，讨论了Grothendieck群K_0中例外向量丛类的一些问题。螺旋线理论的算术问题等价于格上半正交基上的等距群的轨道和辫群的自然作用的轨道的描述。在第三节中，我们讨论了非对称形式及其等距的一般性质，然后在第四节中给出了一些例子。
In this paper we will discuss the connections between the description of the combinatorical structure of the set of exceptional vector bundles and some natural questions about the unimodular (nonsymmetrical) bilinear forms. For investigation of the set of exceptional vector bundles (such bundles that Exti(E, E= 0 for i ≠ 0 and dim Ext0(E, E= 1) there was developed five years ago in [GR], [G1], [G2] the theory of helices. In section 1 we give a review of the main results of this theory. In section 2 we formulate some questions about classes of exceptional vector bundles in Grothendieck groupK0in terms of a lattice with nonsymmetrical nondegenerate integer bilinear form. Arithmetical problems of helix theory are equivalent to the description of the orbits of isometries and orbits of the natural action of braid group on semiorthogonal bases of a lattice. In section 3 we speak about the general properties of nonsymmetrical forms and their isometries and then give some examples in section 4.