Residual finiteness for complexified real line arrangements
英文摘要:
This paper has been withdrawn due to a crucial error in the proof of the main theorem
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
Eriko Hironaka
This paper has been withdrawn due to a crucial error in the proof of the main theorem
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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Given a hyperplane arrangement A in a real vector space, we introduce a real algebraic prevariety Z(A), and exhibit the complement of the complexification of A as the total space of an affine bundle with fibers modeled on the dual of the ambient vector space.
The cohomology groups of finite cyclic covers of complexified real arrangement complements
本文研究复化实构形补空间有限循环覆盖的上同调群,利用Yoshinaga的室上链复形得到贝蒂数上界,引入类CDO组合条件证明此类覆盖整上同调无挠,部分推广了作者与Liu的相关结果。
We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring of polynomials over the number field ${\mathbb Q}(\sqrt{5})$.
Let $\mathcal{A} $ be a complexified-real arrangement of lines in $\mathbb{C}^2.$ Let $H$ be any line in $ \mathcal{A} $. Then, form a new complexified-real arrangement $ \mathcal{B}_H = \mathcal{A} \cup \mathcal{C} $ where $ \mathcal{C} \cup \{H\} $ is a pencil of lines with multiplicity $ m\geq 3 $, the intersection point in the pencil is not a multiple point in $ \mathcal{A}, $ and every line in $ \mathcal{C} $ intersects every line in $ \mathcal{A}\setminus \{H\} $ in points of multiplicity two. In this article, we show that for $ H_1, H_2 \in \mathcal{A} $ we may have that $ \mathcal{B}_{…
Homology of Local Systems on Real Line Arrangement Complements
研究复化实线排列补集的同调群,通过实图确定其维数,给出新的上界,并探讨包含锐对排列的情况,推进了Yoshinaga的猜想。
Milnor fibrations and oriented matroids
该研究利用定向拟阵为复化实排列构造组合模型,得到与米尔诺纤维同伦等价的有限正则CW复形,证明其同伦类型仅依赖定向拟阵结构,且适用于任意定向拟阵。
The homology groups of finite cyclic covering of line arrangement complement
本文研究复线排列补空间有限循环覆盖的第一整同调群,在类似 Cohen-Dimca-Orlik 的条件下证明其无挠,并将 Williams 关于复化线排列的结果推广到任意复线排列。
We study Milnor fibers of complexified real line arrangements. We give a new algorithm computing monodromy eigenspaces of the first cohomology. The algorithm is based on the description of minimal CW-complexes homotopic to the complements, and uses the real figure, that is, the adjacency relations of chambers. It enables us to generalize a vanishing result of Libgober, give new upper-bounds and characterize the $A_3$-arrangement in terms of non-triviality of Milnor monodromy.
Monodromy Eigenvalues of Milnor Fibers for Line Arrangements
本文通过组合消失准则与 Hirzebruch 不等式,证明线排列 Milnor 纤维单值特征值阶数至多五(实排列至多四),推进并证实了相关猜想。
A central question in the study of line arrangements in the complex projective plane $\mathbb{CP}^2$ is: when does the combinatorial data of the arrangement determine its topological properties? In the present work, we introduce a topological invariant of complexified real line arrangements, the chamber weight. This invariant is based on the weight counting over the points of the arrangement dual configuration, located in particular chambers of the real projective plane $\mathbb{RP}^2$, dealing only with geometrical properties. Using this dual point of view, we construct several examples of co…
We give a new algorithm computing local system cohomology groups for complexified real line arrangements. Using it, we obtain several conditions for the first local system cohomology to vanish and to be at most one-dimensional, which generalize a result by Cohen-Dimca-Orlik. The conditions are described in terms of discrete geometric structures of real figures. The proof is based on a recent study on minimal cell structures. We also compute the characteristic variety of the deleted $B_3$-arrangement.
A venerable problem in combinatorics and geometry asks whether a given incidence relation may be realized by a configuration of points and lines. The classic version of this would ask for algebraic lines over some field or possibly real pseudolines: embedded circles (isotopic to $RP^1$) in the real projective plane. In this paper we investigate whether a configuration is realized by a collection of $2$-spheres embedded, in the symplectic, smooth, or topological (locally flat) categories, in the complex projective plane. We find obstructions to realizability in the topological category, which a…
In this survey, we gather together various results on the action of a real form of a complex semisimple Lie group on its flag manifolds. We start with the finiteness theorem of J.Wolf implying that at least one of the orbits is open. We give a new proof of the converse statement for real forms of inner type, essentially due to F.M.Malyshev. Namely, if a real semisimple Lie group of inner type has an open orbit on an algebraic homogeneous space of the complexified group then the homogeneous space is a flag manifold. To prove this, we recall, partly with proofs, some results of A.L.Onishchik on …
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