首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 656 毫秒
1.
Let Y be a compact nonsingular real algebraic set whose homology classes (over Z/2) are represented by Zariski closed subsets. It is well known that every smooth map from a compact smooth manifold to Y is unoriented bordant to a regular map. In this paper, we show how to construct smooth maps from compact nonsingular real algebraic sets to Y not homotopic to any regular map starting from a nonzero homology class of Y of positive degree. We use these maps to obtain obstructions to the existence of local algebraic tubular neighborhoods of algebraic submanifolds of Rn and to study some algebro-homological properties of rational real algebraic manifolds.  相似文献   

2.
We investigate some properties of underlying real algebraic structure on complex projective varieties.  相似文献   

3.
4.
We prove that a continuous map from a compact nonsingular real algebraic variety X into the unit 2-sphere can be approximated by regular maps if and only if it is homotopic to a continuous map which is regular in the complement of a Zariski closed subvariety A of X of codimension at least 3. The assumption on the codimension of A is essential.  相似文献   

5.
LetW be a real algebraic set. We show that the following families of integer-valued functions onW coincide: (i) the functions of the formωλ(X ω ), where X ω are the fibres of a regular morphismf :XW of real algebraic sets, (ii) the functions of the formωχ(X ω ), where X ω are the fibres of a proper regular morphismf :XW of real algebraic sets, (iii) the finite sums of signs of polynomials onW. Such functions are called algebraically constructible onW. Using their characterization in terms of signs of polynomials we present new proofs of their basic functorial properties with respect to the link operator and specialization. Research partially supported by an Australian Research Council Small Grant. Second author also partially supported by KBN 610/P3/94.  相似文献   

6.
This paper deals with a question of Fontaine and Rapoport which was posed in [1]. They asked for the determination of the index set of the Harder-Narasimhan vectors of the filtered isocrystals with fixed Newton- and Hodge vector. The aim of this paper is to give an answer to their question.  相似文献   

7.
Let IG be the toric ideal of a graph G. We characterize in graph theoretical terms the primitive, the minimal, the indispensable and the fundamental binomials of the toric ideal IG.  相似文献   

8.
We reduce the problem of the projective normality of polarized abelian varieties to check the rank of very explicit matrices. This allows us to prove some results on normal generation of primitive line bundles on abelian threefolds and fourfolds. We also give two situations where the projective normality always fails. Finally we make some conjecture. Received: 1 September 2004; revised: 10 March 2005  相似文献   

9.
We show fundamental properties on embedding of abelian surfaces into projective toric 4-folds, and study the case of the toric Del Pezzo 4-fold from the viewpoint of the moduli space of abelian surfaces with polarization of type (1, 5). Received: 31 January 2005; revised: 15 April 2005  相似文献   

10.
11.
Let X be an affine surface admitting a unique affine ruling and a -action. Assume that the ruling has a unique degenerate fibre and that this fibre is irreducible. In this paper we give a short proof of the following result of Miyanishi and Masuda: the universal covering of X is a hypersurface in the affine 3-space given by the equation xmy = zd − 1, where m > 1. Received: 13 June 2005  相似文献   

12.
For everyt>1 and positiven we construct explicit examples of graphsG with |V (G)|=n, |E(G)|c t ·n 2–1/t which do not contain a complete bipartite graghK t,t !+1 This establishes the exact order of magnitude of the Turán numbers ex (n, K t,s ) for any fixedt and allst!+1, improving over the previous probabilistic lower bounds for such pairs (t, s). The construction relies on elementary facts from commutative algebra.Research supported in part by NSF Grants DMS-8707320 and DMS-9102866.Research supported in part by Hungarian National Foundation for Scientific Research Grant  相似文献   

13.
We study the projective space of univariate rational parameterized equations of degree d or less in real projective space The parameterized equations of degree less than d form a special algebraic variety We investigate the subspaces on and their relation to rational curves in give a geometric characterization of the automorphism group of and outline applications of the theory to projective kinematics.  相似文献   

14.
Let XP be a smooth projective toric variety of dimension n embedded in Pr using all of the lattice points of the polytope P. We compute the dimension and degree of the secant variety . We also give explicit formulas in dimensions 2 and 3 and obtain partial results for the projective varieties XA embedded using a set of lattice points APZn containing the vertices of P and their nearest neighbors.  相似文献   

15.
Let R be a commutative noetherian local ring and consider the set of isomorphism classes of indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it has exactly one element, represented by the rank 1 free module, or R is Gorenstein and an isolated singularity (if R is complete, then it is even a simple hypersurface singularity). The crux of our proof is to argue that if the residue field has a totally reflexive cover, then R is Gorenstein or every totally reflexive R-module is free.  相似文献   

16.
17.
Tropical geometry yields good lower bounds, in terms of certain combinatorial-polyhedral optimisation problems, on the dimensions of secant varieties. The approach is especially successful for toric varieties such as Segre-Veronese embeddings. In particular, it gives an attractive pictorial proof of the theorem of Hirschowitz that all Veronese embeddings of the projective plane except for the quadratic one and the quartic one are non-defective; and indeed, no Segre-Veronese embeddings are known where the tropical lower bound does not give the correct dimension. Short self-contained introductions to secant varieties and the required tropical geometry are included.  相似文献   

18.
Every normal complex surface singularity with -homology sphere link has a universal abelian cover. It has been conjectured by Neumann and Wahl that the universal abelian cover of a rational or minimally elliptic singularity is a complete intersection singularity defined by a system of ``splice diagram equations'. In this paper we introduce a Neumann-Wahl system, which is an analogue of the system of splice diagram equations, and prove the following. If (X, o) is a rational or minimally elliptic singularity, then its universal abelian cover (Y, o) is an equisingular deformation of an isolated complete intersection singularity (Y0, o) defined by a Neumann-Wahl system. Furthermore, if G denotes the Galois group of the covering YX, then G also acts on Y0 and X is an equisingular deformation of the quotient Y0/G. Dedicated to Professor Jonathan Wahl on his sixtieth birthday. This research was partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan.  相似文献   

19.
Let p≥5 be a prime, ζ a primitive pth root of unity and λ=1−ζ. For 1≤sp−2, the smooth projective model Cp,s of the affine curve vp=us(1−u) is a curve of genus (p−1)/2 whose jacobian Jp,s has complex multiplication by the ring of integers of the cyclotomic field Q(ζ). In 1981, Greenberg determined the field of rationality of the p-torsion subgroup of Jp,s and moreover he proved that the λ3-torsion points of Jp,s are all rational over Q(ζ). In this paper we determine quite explicitly the λ3-torsion points of Jp,1 for p=5 and p=7, as well as some further p-torsion points which have interesting arithmetical applications, notably to the complementary laws of Kummer’s reciprocity for pth powers.  相似文献   

20.
Let R be a regular noetherian local ring of dimension n≥2 and (Ri)≡R=R0R1R2⊂?⊂Ri⊂? be a sequence of successive quadratic transforms along a regular prime ideal p of R (i.e if pi is the strict transform of p in Ri, then piRi, i≥0). We say that p is maximal for (Ri) if for every non-negative integer j≥0 and for every prime ideal qj of Rj such that (Ri) is a quadratic sequence along qj with pjqj, we have pj=qj. We show that p is maximal for (Ri) if and only if V=∪i≥0Ri/pi is a valuation ring of dimension one. In this case, the equimultiple locus at p is the set of elements of the maximal ideal of R for which the multiplicity is stable along the sequence (Ri), provided that the series of real numbers given by the multiplicity sequence associated with V diverges. Furthermore, if we consider an ideal J of R, we also show that is normally flat along at the closed point if and only if the Hironaka’s character ν(J,R) is stable along the sequence (Ri). This generalizes well known results for the case where p has height one (see [B.M. Bennett, On the characteristic functions of a local ring, Ann. of Math. Second Series 91 (1) (1970) 25-87]).  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号