共查询到20条相似文献,搜索用时 31 毫秒
1.
Motivic integration [M. Kontsevich, Motivic integration, Lecture at Orsay, 1995] and MacPherson's transformation [R. MacPherson, Chern classes for singular varieties, Ann. of Math. 100 (1974) 423-432] are combined in this paper to construct a theory of “stringy” Chern classes for singular varieties. These classes enjoy strong birational invariance properties, and their definition encodes data coming from resolution of singularities. The singularities allowed in the theory are those typical of the minimal model program; examples are given by quotients of manifolds by finite groups. For the latter an explicit formula is proven, assuming that the canonical line bundle of the manifold descends to the quotient. This gives an expression of the stringy Chern class of the quotient in terms of Chern-Schwartz-MacPherson classes of the fixed-point set data. 相似文献
2.
Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with
arbitrary Kawamata log-terminal pairs. There is a natural Kawamata log-terminal pair corresponding to an algebraic variety
V having a regular action of a finite group G. In this situation we show that the stringy Euler number of this pair coincides
with the physicists’ orbifold Euler number defined by the Dixon-Harvey-Vafa-Witten formula. As an application, we prove a
conjecture of Miles Reid on the Euler numbers of crepant desingularizations of Gorenstein quotient singularities.
Received March 19, 1998 相似文献
3.
For two complex vector bundles admitting a homomorphism with isolated singularities between them, we establish a Poincaré–Hopf type formula for the difference of the Chern character numbers of these two vector bundles. As a consequence, we extend the original Poincaré–Hopf index formula to the case of complex vector fields. 相似文献
4.
Fabian Langholf 《Mathematische Nachrichten》2013,286(13):1305-1325
We prove an explicit formula for the truncated Atiyah class of a bounded complex of vector bundles. Furthermore, we show that the first truncated Chern class of such a complex only depends on its determinant. 相似文献
5.
Some method is proposed for finding Ein components in moduli spaces of stable rank 2 vector bundles with first Chern class c1 = 0 on the projective 3-space. We formulate and illustrate a conjecture on the growth rate of the number of Ein components in dependence on the numbers of the second Chern class. We present a method for calculating the spectra of the above bundles, a recurrent formula, and an explicit formula for computing the number of the spectra of these bundles. 相似文献
6.
Georg Hein 《Journal of Geometry》2004,79(1-2):89-101
We develop a formula (Theorem 5.2) which allows to compute top Chern classes of
vector bundles on the vanishing locus V(s) of a section of this bundle. This
formula particularly applies in the case when V(s) is the union of local complete
intersections giving the individual contribution of each component and their mutual
intersections. We conclude with applications to the enumeration of rational curves in
complete intersections in projective space. 相似文献
7.
Lars Allermann 《Arkiv f?r Matematik》2012,50(2):237-258
We introduce tropical vector bundles, morphisms and rational sections of these bundles and define the pull-back of a tropical vector bundle and of a rational section along a morphism. Most of the definitions presented here for tropical vector bundles will be contained in Torchiani, C., Line Bundles on Tropical Varieties, Diploma thesis, Technische Universität Kaiserslautern, Kaiserslautern, 2010, for the case of line bundles. Afterwards we use the bounded rational sections of a tropical vector bundle to define the Chern classes of this bundle and prove some basic properties of Chern classes. Finally we give a complete classification of all vector bundles on an elliptic curve up to isomorphisms. 相似文献
8.
Zhi Lan Wang 《数学学报(英文版)》2016,32(8):901-910
We propose a conjecture on the generating series of Chern numbers of tautological bundles on symmetric products of curves and establish the rank 1 and rank -1 case of this conjecture. Thus we compute explicitly the generating series of integrals of Segre classes of tautological bundles of line bundles on curves, which has a similar structure as Lehn's conjecture for surfaces. 相似文献
9.
We describe the Chern classes of holomorphic vector bundles on non-algebraic complex torus of dimension 2. 相似文献
10.
Carlo Perrone 《Mathematische Annalen》2009,345(1):83-132
We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Beside a study of the general properties of such a cohomology, we show that, given a complex vector bundle, one can compute its topological Chern classes using the extendable Chern classes, defined via a Chern–Weil type theory. We also prove that the localizations of the extendable Chern classes represent the localizations of the respective topological Chern classes, thus obtaining an abstract residue theorem for compact singular complex analytic varieties. As an application of our theory, we prove a Camacho–Sad type index theorem for holomorphic foliations of singular complex varieties. 相似文献
11.
Luis Fuentes García 《Archiv der Mathematik》2005,85(5):409-418
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
12.
We prove a new formula for the Hirzebruch–Milnor classes of global complete intersections with arbitrary singularities describing the difference between the Hirzebruch classes and the virtual ones. This generalizes a formula for the Chern–Milnor classes in the hypersurface case that was conjectured by S. Yokura and was proved by A. Parusiński and P. Pragacz. It also generalizes a formula of J. Seade and T. Suwa for the Chern–Milnor classes of complete intersections with isolated singularities. 相似文献
13.
Seung Jin Lee 《Journal of Algebraic Combinatorics》2018,47(2):213-231
We discuss a relationship between Chern–Schwartz–MacPherson classes for Schubert cells in flag manifolds, the Fomin–Kirillov algebra, and the generalized nil-Hecke algebra. We show that the nonnegativity conjecture in the Fomin–Kirillov algebra implies the nonnegativity of the Chern–Schwartz–MacPherson classes for Schubert cells in flag manifolds for type A. Motivated by this connection, we also prove that the (equivariant) Chern–Schwartz–MacPherson classes for Schubert cells in flag manifolds are certain summations of the structure constants of the equivariant cohomology of Bott–Samelson varieties. We also discuss refined positivity conjectures of the Chern–Schwartz–MacPherson classes for Schubert cells motivated by the nonnegativity conjecture in the Fomin–Kirillov algebra. 相似文献
14.
Denote by T1 the vector space of infinitesimal deformations of a dihedral singularity of type Dn, q. Using Pinkham's method for quotient surface singularities we prove a formula for dim T1. 相似文献
15.
Laura Costa 《manuscripta mathematica》1999,100(3):335-349
Let be a ruled Fano 3-fold. The goal of this paper is to compute the dimension, prove the irreducibility and smoothness and describe
the structure of the moduli space M
L
(2;c
1,c
2) of L-stable, rank 2 vector bundles E on X with certain Chern classes and for a suitable polarization L closely related to c
2. More precisely, we will cover the study of some moduli spaces M
L
(2;c
1,c
2) such that the generic point is given as a non-trivial extension of line bundles. This work nicely reflects the general philosophy that moduli spaces
inherits a lot of geometrical properties of the underlying variety.
Received: 16 February 1999 / Revised version: 2 July 1999 相似文献
16.
Sukmoon Huh 《Journal of Pure and Applied Algebra》2011,215(9):2099-2105
We prove that the moduli space of stable sheaves of rank 2 with the Chern classes c1=OQ(1,1) and c2=2 on a smooth quadric Q in P3 is isomorphic to P3. Using this identification, we give a new proof that a Brill-Noether locus, defined as the closure of the stable bundles with at least three linearly independent sections, on a non-hyperelliptic curve of genus 4, is isomorphic to the Donagi-Izadi cubic threefold. 相似文献
17.
18.
Marcos Jardim 《Bulletin of the Brazilian Mathematical Society》2007,38(4):649-659
Using monads, we construct a large class of stable bundles of rank 2 and 3 on 3-fold hypersurfaces, and study the set of all
possible Chern classes of stable vector bundles. 相似文献
19.
Jaya N. N. Iyer 《Mathematische Zeitschrift》2008,260(1):61-76
In this note, we investigate the cycle class map between the rational Chow groups and the arithmetic Deligne cohomology, introduced
by Green–Griffiths and Asakura–Saito. We show nontriviality of the Chern classes of flat bundles in the arithmetic Deligne
Cohomology in some cases and our proofs also indicate that generic flat bundles can be expected to have nontrivial classes.
This provides examples of non-zero classes in the arithmetic Deligne cohomology which become zero in the usual rational Deligne
cohomology. 相似文献
20.
B. Anchouche 《manuscripta mathematica》1999,100(4):423-436
We show that over some smooth projective varieties every semistable Higgs logarithmic vector bundle is semistable in the ordinary
sense, hence satisfies Bogomolov inequality. More generaly, we prove that semistable Higgs parabolic vector bundles of rank
two over smooth projective varieties of dimension ≥ 2 satisfy the “parabolic” 'Bogomolov inequality
Received: 1 March 1999 / Revised version: 11 June 1999 相似文献