共查询到20条相似文献,搜索用时 15 毫秒
1.
Mathias Lederer 《Journal of Pure and Applied Algebra》2008,212(5):1116-1133
Given a finite set of closed rational points of affine space over a field, we give a Gröbner basis for the lexicographic ordering of the ideal of polynomials which vanish at all given points. Our method is an alternative to the Buchberger-Möller algorithm, but in contrast to that, we determine the set of leading terms of the ideal without solving any linear equation but by induction over the dimension of affine space. The elements of the Gröbner basis are also computed by induction over the dimension, using one-dimensional interpolation of coefficients of certain polynomials. 相似文献
2.
Haibao Duan 《Advances in Mathematics》2003,180(1):112-133
We study integration along Bott-Samelson cycles. As an application the degree of a Schubert variety on a flag manifold G/B is evaluated in terms of certain Cartan numbers of G. 相似文献
3.
In this paper we show that the image of any locally finite k-derivation of the polynomial algebra k[x,y] in two variables over a field k of characteristic zero is a Mathieu subspace. We also show that the two-dimensional Jacobian conjecture is equivalent to the statement that the image of every k-derivation D of k[x,y] such that and is a Mathieu subspace of k[x,y]. 相似文献
4.
We study polynomial endomorphisms F of CN which are locally finite in the following sense: the vector space generated by r°Fn (n≥0) is finite dimensional for each r∈C[x1,…,xN]. We show that such endomorphisms exhibit similar features to linear endomorphisms: they satisfy the Jacobian Conjecture, have vanishing polynomials, admit suitably defined minimal and characteristic polynomials, and the invertible ones admit a Dunford decomposition into “semisimple” and “unipotent” constituents. We also explain a relationship with linear recurrent sequences and derivations. Finally, we give particular attention to the special cases where F is nilpotent and where N=2. 相似文献
5.
After the contributions of Furushima, Nakayama, Peternell and Schneider, in 1993, Furushima [Fur93] finally succeeded in the
classification of the compactifications of the affine 3-space into smooth Fano 3-folds with B2=1. In this paper, we consider the compactifications of the contractible affine 3-folds X (not necessarily X=) into smooth Fano 3-folds V with B2=2. Consequently, we classify all such compactifications X↪(V,D1∪D2) in the case where KV+D1+D2 is not nef. Furthermore, we see that infinitely many mutually non-isomorphic exotic 's can be compactified into Fano 3-folds with B2=2. This phenomenon never occurs when B2=1.
During this research the author was supported as a Twenty-First Century COE Kyoto Mathematics Fellow. 相似文献
6.
Let p be a prime and let be a primitive p-th root of unity. For a finite extension k of containing , we consider a Kummer extension of degree p. In this paper, we show that if and the class number of k is one, the index of is one. We also show that if is tamely ramified with a normal integral basis, the index is at most a power of p. In the last section, we show that there exist infinitely many cubic Kummer extensions of for both wildly and tamely ramified cases, whose integer rings do not have a power integral basis over that of . 相似文献
7.
Charles Ching-An Cheng 《Journal of Pure and Applied Algebra》2005,195(2):127-130
Let R be a field with characteristic zero. In this paper it is proved that power linear Keller maps Rn→Rn with rank at most two are linearly triangularizable. 相似文献
8.
Let Λ be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of Λ is zero in Λ. Let T(Λ)=Λ?D(Λ) be the trivial extension of Λ by its minimal injective cogenerator D(Λ). We characterize, in terms of quivers and relations, the algebras Λ′ such that T(Λ)?T(Λ′). 相似文献
9.
We provide an explicit algorithm of computing the mapping degree of a rational mapping from the real projective line to itself.
As a corollary we prove Sturm’s theorem and a number of its generalizations. These generalizations are used to prove Tarski’s
theorem about real semialgebraic sets. Similarly a version of Tarski’s theorem can be proved for an arbitrary algebraically
closed field.
To V. I. Arnold on the occasion of his 70th birthday 相似文献
10.
It is well-known that an element of the linear group is semisimple if and only if its conjugacy class is Zariski closed. The aim of this paper is to show that the same result holds for the group of complex plane polynomial automorphisms. 相似文献
11.
Xiaosong Sun 《Journal of Pure and Applied Algebra》2010,214(11):1962-1972
In this paper, we describe the structure of quadratic homogeneous quasi-translations, and we prove that, in dimension 9 and less, such a map is linearly triangularizable, or equivalently a quadratic homogeneous nice derivation is linearly conjugate to a triangular derivation. 相似文献
12.
Pierrette Cassou-Noguès 《Journal of Pure and Applied Algebra》2009,213(5):711-723
Let φ=(f,g) be an endomorphism of the affine plane C2 defined by two polynomials f,g∈C[x,y] and let Λ={Cb∣b∈C} be the pencil of lines Cb defined by x=b. We shall consider the smoothness criterion of the image curve φ(Cb). The hypersurface V whose coordinate ring is C[x,f,g] and the normalization of V will play interesting roles in analyzing the properties of the set φ(Λ)={φ(Cb)∣b∈C}. 相似文献
13.
14.
Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 相似文献
15.
Let A be the local ring at a point of a normal complex variety with completion . Srinivas has asked about the possible images of the induced map over all geometric local normal domains A with fixed completion R. We use Noether–Lefschetz theory to prove that all finitely generated subgroups are possible in some familiar cases. As a byproduct we show that every finitely generated abelian group appears as the class group of the local ring at the vertex of a cone over some smooth complex variety of each positive dimension. 相似文献
16.
We show that if L/
K is a degree p
extension of number fields which is wildly ramified at a prime ${\frak p}$ of
K of residue characteristic
p, then the ramification groups of ${\frak p}$
(in the splitting field of L over
K) are uniquely determined by the
${\frak p}$-adic valuation of the discriminant of L
/K.Received: 3 July 2002 相似文献
17.
According to a conjecture of H. Clemens, the dimension of the space of rational curves on a general projective hypersurface should equal the number predicted by a naïve dimension count. In the case of a general hypersurface of degree 7 in P5, the conjecture predicts that the only rational curves should be lines. This has been verified by Hana and Johnsen for rational curves of degree at most 15. Here we extend their results to show that no rational curves of degree 16 lie on a general heptic fourfold. 相似文献
18.
Zbigniew Jelonek 《Mathematische Annalen》1999,315(1):1-35
In this paper we characterize testing sets for properness of polynomial mappings . We also study the set of points at which such mappings are not proper. As the first application we give a proof of the Complementary Conjecture of McKay and Wang (Conjecture 12 in [16]). The second application is an answer to the problem of Kraft- Russell about a characterization of The third application is (given in [13]) a solution of the Problem of Van den Essen and Shpilrain about endomorphism of the ring The fourth application is a theorem about extensions of affine varieties. Received: 27 February 1998 / in revised form: 10 January 1999 相似文献
19.
Marta Pérez Rodríguez 《Journal of Pure and Applied Algebra》2008,212(11):2381-2388
We provide the main results of a deformation theory of smooth formal schemes as defined in [L. Alonso Tarrío, A. Jeremías López, M. Pérez Rodríguez, Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes, Comm. Algebra 35 (2007) 1341-1367]. Smoothness is defined by the local existence of infinitesimal liftings. Our first result is the existence of an obstruction in a certain Ext1 group whose vanishing guarantees the existence of global liftings of morphisms. Next, given a smooth morphism f0:X0→Y0 of noetherian formal schemes and a closed immersion Y0?Y given by a square zero ideal I, we prove that the set of isomorphism classes of smooth formal schemes lifting X0 over Y is classified by and that there exists an element in which vanishes if and only if there exists a smooth formal scheme lifting X0 over Y. 相似文献
20.
In this paper we completely classify all polynomial maps of the form H=(u(x,y),v(x,y,z),h(u(x,y),v(x,y,z))) with JH nilpotent. 相似文献