共查询到20条相似文献,搜索用时 31 毫秒
1.
Ivan PaninSerge Yagunov 《Journal of Pure and Applied Algebra》2002,172(1):49-77
In the following paper we introduce the notion of orientable functor (orientable cohomology theory) on the category of projective smooth schemes and define a family of transfer maps. Applying this technique, we prove that with finite coefficients orientable cohomology of a projective variety is invariant with respect to the base-change given by an extension of algebraically closed fields. This statement generalizes the classical result of Suslin, concerning algebraic K-theory of algebraically closed fields. Besides K-theory, we treat such examples of orientable functors as etale cohomology, motivic cohomology, algebraic cobordism. We also demonstrate a method to endow algebraic cobordism with multiplicative structure and Chern classes. 相似文献
2.
S. Zubė 《Lithuanian Mathematical Journal》1998,38(3):291-308
The main purpose of this paper is to study projective classes of bidegree (2,1) parametrizable surfaces in a real projective
3-space. It turns out that the implicit degree of such surfaces is two, three, or four, and singular curves have degree three.
We describe all possibilities for singular curves and pinch points on such surfaces. The presentation has been made from the
point of view of analytic geometry and does not presume a deep knowledge of algebraic geometry.
Partially supported by the Lithuanian State Science and Studies Foundation.
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 38, No. 3, pp.
379–402, July–September, 1998. 相似文献
3.
In this paper we consider second order scalar elliptic boundary value problems posed over three–dimensional domains and their
discretization by means of mixed Raviart–Thomas finite elements [18]. This leads to saddle point problems featuring a discrete
flux vector field as additional unknown. Following Ewing and Wang [26], the proposed solution procedure is based on splitting
the flux into divergence free components and a remainder. It leads to a variational problem involving solenoidal Raviart–Thomas
vector fields. A fast iterative solution method for this problem is presented. It exploits the representation of divergence
free vector fields as s of the –conforming finite element functions introduced by Nédélec [43]. We show that a nodal multilevel splitting of these finite
element spaces gives rise to an optimal preconditioner for the solenoidal variational problem: Duality techniques in quotient
spaces and modern algebraic multigrid theory [50, 10, 31] are the main tools for the proof.
Received November 4, 1996 / Revised version received February 2, 1998 相似文献
4.
We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties.
For a given toric variety X we first construct a toric quasi–projective reduction. Then we show that X has a quasi–projective reduction if and only if its toric quasi–projective reduction is surjective. We apply this result
to characterize when the action of a subtorus on a quasi–projective toric variety admits a categorical quotient in the category
of quasi–projective varieties.
Received October 29, 1998; in final form December 28, 1998 相似文献
5.
A. Nenashev 《Journal of Pure and Applied Algebra》2006,205(2):323-340
For an oriented cohomology theory A and a relative cellular space X, we decompose the A-motive of X into a direct sum of twisted motives of the base spaces. We also obtain respective decompositions of the A-cohomology of X. Applying them, one can compute A(X), where X is an isotropic projective homogeneous variety and A means algebraic K-theory, motivic cohomology or algebraic cobordism MGL. 相似文献
6.
7.
Christopher Manon 《Journal of Algebraic Combinatorics》2010,31(4):467-489
We study presentations for subalgebras of invariants of the coordinate algebras of binary symmetric models of phylogenetic
trees studied by Buczynska and Wisniewski in (J. Eur. Math. Soc. 9:609–635, 2007). These algebras arise as toric degenerations of projective coordinate rings of the moduli of weighted points on the projective
line, and projective coordinate rings of the moduli of quasiparabolic semisimple rank two bundles on the projective line. 相似文献
8.
We consider a perturbed Hermitian–Einstein equation, which we call the Donaldson–Thomas equation, on compact Kähler threefolds. In [12], we analysed some analytic properties of solutions to the equation, in particular, we proved that a sequence of solutions to the Donaldson–Thomas equation has a subsequence which smoothly converges to a solution to the Donaldson–Thomas equation outside a closed subset of the Hausdorff dimension two. In this article, we prove that some of these singularities can be removed. 相似文献
9.
K. Menger and G. Birkhoff recognized 70 years ago that lattice theory provides a framework for the development of incidence
geometry (affine and projective geometry). We show in this article that lattice theory also provides a framework for the development
of metric geometry (including the euclidean and classical non-euclidean geometries which were first discovered by A. Cayley
and F. Klein). To this end we introduce and study the concept of a Cayley–Klein lattice. A detailed investigation of the groups
of automorphisms and an algebraic characterization of Cayley–Klein lattices are included.
The authors would like to thank an unknown referee for his helpful suggestions. 相似文献
10.
Gereon Quick 《Advances in Mathematics》2007,214(2):730-760
We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an étale topological realization of the stable A1-homotopy theory of smooth schemes over a base field of arbitrary characteristic in analogy to the complex realization functor for fields of characteristic zero.On the other hand we get a natural setting for étale cohomology theories. In particular, we define and discuss an étale topological cobordism theory for schemes. It is equipped with an Atiyah-Hirzebruch spectral sequence starting from étale cohomology. Finally, we construct maps from algebraic to étale cobordism and discuss algebraic cobordism with finite coefficients over an algebraically closed field after inverting a Bott element. 相似文献
11.
T. E. Panov 《Proceedings of the Steklov Institute of Mathematics》2008,263(1):150-162
In the theory of algebraic group actions on affine varieties, the concept of a Kempf-Ness set is used to replace the categorical
quotient by the quotient with respect to a maximal compact subgroup. Using recent achievements of “toric topology,” we show
that an appropriate notion of a Kempf-Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate
subspace arrangement complements) arising in the Batyrev-Cox “geometric invariant theory” approach to toric varieties. We
proceed by studying the cohomology of these “toric” Kempf-Ness sets. In the case of projective nonsingular toric varieties
the Kempf-Ness sets can be described as complete intersections of real quadrics in a complex space.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 263, pp. 159–172. 相似文献
12.
G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kähler metric of constant scalar curvature. In [D3] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson’s results and computations to a new case, that of reductive varieties.Received: November 2003 Revision: January 2004 Accepted: January 2004 相似文献
13.
Chen Xigeng 《东北数学》1997,(1)
SmoothInvolutionsonthe2k┐dimensionalQuaternionicProjectiveSpaceHP(2k)ChenXigeng(陈锡庚)andPengJinxiang(彭金祥)(DepartmentofMathemat... 相似文献
14.
We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a parameterized version of a theorem by Joseph Gubeladze; we show that if M is a countable, abelian, cancellative, torsion-free, semi-normal monoid, and X is contractible, then every finitely generated projective module over C(X)[M] is free. The particular case gives a parameterized version of the celebrated theorem proved independently by Daniel Quillen and Andrei Suslin that finitely
generated projective modules over a polynomial ring over a field are free. The conjecture of Jonathan Rosenberg which predicts
the homotopy invariance of the negative algebraic K-theory of C(X) follows from the particular case . We also give algebraic conditions for a functor from commutative algebras to abelian groups to be homotopy invariant on
C
*-algebras, and for a homology theory of commutative algebras to vanish on C
*-algebras. These criteria have numerous applications. For example, the vanishing criterion applied to nil K-theory implies that commutative C
*-algebras are K-regular. As another application, we show that the familiar formulas of Hochschild–Kostant–Rosenberg and Loday–Quillen for
the algebraic Hochschild and cyclic homology of the coordinate ring of a smooth algebraic variety remain valid for the algebraic
Hochschild and cyclic homology of C(X). Applications to the conjectures of Beĭlinson-Soulé and Farrell–Jones are also given. 相似文献
15.
《Journal of Pure and Applied Algebra》2022,226(6):106977
The purpose of this article is to show that the bivariant algebraic A-cobordism groups considered previously by the author are independent of the chosen base ring A. This result is proven by analyzing the bivariant ideal generated by the so called snc relations, and, while the alternative characterization we obtain for this ideal is interesting by itself because of its simplicity, perhaps more importantly it allows us to easily extend the definition of bivariant algebraic cobordism to divisorial Noetherian derived schemes of finite Krull dimension. As an interesting corollary, we define the corresponding homology theory called algebraic bordism. We also generalize projective bundle formula, the theory of Chern classes, the Conner–Floyd theorem and the Grothendieck–Riemann–Roch theorem to this setting. The general definitions of bivariant cobordism are based on the careful study of ample line bundles and quasi-projective morphisms of Noetherian derived schemes, also undertaken in this work. 相似文献
16.
Eric Katz 《Expositiones Mathematicae》2009,27(1):1-36
We give an introduction to Tropical Geometry and prove some results in tropical intersection theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of degenerations of varieties using projective not-necessarily-normal toric varieties. The second part is a foundational account of tropical intersection theory with proofs of some new theorems relating it to classical intersection theory. 相似文献
17.
Raphaël Fino 《Central European Journal of Mathematics》2013,11(6):1068-1077
We prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. These results have already been obtained by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2. 相似文献
18.
Greg Friedman 《Israel Journal of Mathematics》2008,163(1):139-188
We study cobordisms and cobordisms rel boundary of PL locally-flat disk knots D
n−2 ↪ D
n
. Any two disk knots are cobordant if the cobordisms are not required to fix the boundary sphere knots, and any two even-dimensional
disk knots with isotopic boundary knots are cobordant rel boundary. However, the cobordism rel boundary theory of odd-dimensional
disk knots is more subtle. Generalizing results of J. Levine on the cobordism of sphere knots, we define disk knot Seifert
matrices and show that two higher-dimensional disk knots with isotopic boundaries are cobordant rel boundary if and only if
their disk knot Seifert matrices are algebraically cobordant. We also ask which algebraic cobordism classes can be realized
given a fixed boundary knot and provide a complete classification when the boundary knot has no 2-torsion in its middle-dimensional
Alexander module.
In the course of this classification, we establish a close connection between the Blanchfield pairing of a disk knot and the
Farber-Levine torsion pairing of its boundary knot (in fact, for disk knots satisfying certain connectivity assumptions, the
disk knot Blanchfield pairing will determine the boundary Farber-Levine pairing). In addition, we study the dependence of
disk knot Seifert matrices on choices of Seifert surface, demonstrating that all such Seifert matrices are rationally S-equivalent, but not necessarily integrally S-equivalent. 相似文献
19.
Luca Scala 《Geometriae Dedicata》2009,139(1):313-329
We study tautological sheaves on the Hilbert scheme of points on a smooth quasi-projective algebraic surface by means of the
Bridgeland–King–Reid transform. We obtain Brion–Danila’s Formulas for the derived direct image of tautological sheaves or
their double tensor product for the Hilbert–Chow morphism; as an application we compute the cohomology of the Hilbert scheme
with values in tautological sheaves or in their double tensor product, thus generalizing results previously obtained for tautological
bundles.
相似文献
20.
We extend a constructive proof of the Eisenbud–Evans–Storch theorem, developed in a previous work by Coquand, Schuster, and Lombardi, from the affine to the projective case. The main tool is that of distributive lattices, which allows us to replace the classical topological arguments by more algebraic and constructive ones. Given a suitable graded ring, we work in the distributive lattice in which the prime filters correspond to the homogeneous prime ideals. The proof presented here is one of the first examples of concrete results obtained using this tool. 相似文献