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1.
James D. Lewis 《K-Theory》2002,25(3):277-298
Let X/_C be a projective algebraic manifold. In the first part of this paper, we construct a natural real regulator on the cohomology of a Gersten–Milnor complex, and where appropriate, compare it to the Beilinson regulator into real Deligne cohomology. The second part is devoted to a calculation on curves. In particular, we arrive at an elementary new proof of the known nontriviality of the regulator on CH2(X,2), for a general elliptic curve X. Further, if X P 2 is a general curve of degree 3, then for any open Riemann surface U contained in the complement , we arrive at a nontrivial regulator calculation on CH2(U,2). We conclude this paper with an application to points of finite order on a curve X.  相似文献   

2.
In this paper we study Milnor fibrations associated to real isolated singularities defined by map-germs f: (m,0)(2,0). The main result relates the existence of the Milnor fibration with the (C)-regularity of the family of hypersurfaces with isolated singularity obtained by projecting f into the family L of all lines through the origin in the plane 2.  相似文献   

3.
On Milnor Fibrations of Arrangements   总被引:3,自引:0,他引:3  
We use covering space theory and homology with local coefficientsto study the Milnor fiber of a homogeneous polynomial. Thesetechniques are applied in the context of hyperplane arrangements,yielding an explicit algorithm for computing the Betti numbersof the Milnor fiber of an arbitrary real central arrangementin C3, as well as the dimensions of the eigenspaces of the algebraicmonodromy. We also obtain combinatorial formulas for these invariantsof the Milnor fiber of a generic arrangement of arbitrary dimensionusing these methods.  相似文献   

4.
Chulkov  S. P. 《Mathematical Notes》2002,71(5-6):871-874
Mathematical Notes -  相似文献   

5.
Functional Analysis and Its Applications - In this paper we study relationships between some topological and analytic invariants of zero-dimensional germs, or multiple points. Among other things,...  相似文献   

6.
Given a polynomial with real coefficients, we produce a motivic analog of a simple identity that relates the complex conjugation and the monodromy of the Milnor fibre of its complexification. To that purpose, we introduce motivic zeta functions that take into account complex conjugation and monodromy.  相似文献   

7.
We analyze the monodromy action, over the rationals, on the first homology group of the Milnor fiber, for arbitrary subarrangements of Coxeter arrangements. We propose a combinatorial formula for the monodromy action, involving Aomoto complexes in positive characteristic. We verify the formula, in cases A, B and D.  相似文献   

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In memoriam Deane Montgomery  相似文献   

12.
Jinya Nakamura 《K-Theory》2000,19(3):269-309
For a complete discrete valuation field K, the unit group of K has a natural decreasing filtration with respect to the valuation, and the graded quotients of this filtration are written in terms of the residue field. The Milnor K-group of a field is a generalization of the unit group. The Milnor K-group of K has a natural decreasing filtration of the same kind. However, if K is of mixed characteristics and has an absolute ramification index greater than one, the structure is not yet known. The aim of this paper is to determine the structure of the Milnor K-group of some special K, which are of mixed characteristics (0,p), whose residue fields are allowed to be imperfect, and which are of absolute ramification index p(p–1).  相似文献   

13.
Piotr Jaworski 《K-Theory》1996,10(1):83-105
Let V be a quasihomogeneous normal variety. The aim of this paper is to describe the Milnor K-theory of the function field of V in terms of the second residue homomorphisms associated with subvarieties and resolution data of V.Supported by KBN, 2 P301 010 06.  相似文献   

14.
该文研究了黎曼齐次空间G/H中子流形M~p和子流形N~q的交M~p∩gN~q的测地曲率,其中g∈G为等距群,并把M~p∩gN~q的第二基本形式表示成M~p和N~q的测地曲率以及它们之间的夹角的组合.  相似文献   

15.
Let Hj(K, ·) be the j – th elementary symmetric function of the principal curvatures of a convex body K in Euclidean d – space. We show that the functionals ∫bd f(Hj(K, x)) dℋ︁d—1(x) depend upper semicontinuously on K, if f : [0, ∞) is concave, limt→0f(t) = 0, and limt→∞f(t)/t = 0. An analogous statement holds for integrals of elementary symmetric functions of the principal radii of curvature.  相似文献   

16.
We show that every \(\mu \)-constant family of isolated hypersurface singularities satisfying a nondegeneracy condition in the sense of Kouchnirenko, is topologically trivial, also is equimultiple.  相似文献   

17.
M. Somekawa 《K-Theory》1990,4(2):105-119
In this paper we define and study a Milnor K-group attached to a finite family of semi-Abelian varieties over a field, which is a generalization of the usual Milnor K-group. Using this group, we generalize the work of Bloch.  相似文献   

18.
In this note we study a problem of A'Campo about the minimal non-zero difference between the Milnor numbers of a germ of plane curve and one of its deformation.  相似文献   

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Let \( \Phi : (\mathbb {C}^2, 0) \rightarrow ( \mathbb {C}^3, 0) \) be a finitely determined complex analytic germ and let \((\{f=0\},0)\) be the reduced equation of its image, a non-isolated hypersurface singularity. We provide the plumbing graph of the boundary of the Milnor fibre of f from the double-point-geometry of \(\Phi \).  相似文献   

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