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1.
Edoardo Ballico Francesco Malaspina Paolo Valabrega Mario Valenzano 《Central European Journal of Mathematics》2012,10(4):1361-1379
Let E be an indecomposable rank two vector bundle on the projective space ℙ
n
, n ≥ 3, over an algebraically closed field of characteristic zero. It is well known that E is arithmetically Buchsbaum if and only if n = 3 and E is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically
Buchsbaum vector bundles on the smooth quadric hypersurface Q
n
⊂ ℙ
n+1, n ≥ 3. We give in fact a full classification and prove that n must be at most 5. As to k-Buchsbaum rank two vector bundles on Q
3, k ≥ 2, we prove two boundedness results. 相似文献
2.
Elin Götmark 《Arkiv f?r Matematik》2008,46(1):43-68
We present a method of finding weighted Koppelman formulas for (p,q)-forms on n-dimensional complex manifolds X which admit a vector bundle of rank n over X×X, such that the diagonal of X×X has a defining section. We apply the method to ℙ
n
and find weighted Koppelman formulas for (p,q)-forms with values in a line bundle over ℙ
n
. As an application, we look at the cohomology groups of (p,q)-forms over ℙ
n
with values in various line bundles, and find explicit solutions to the -equation in some of the trivial groups. We also look at cohomology groups of (0,q)-forms over ℙ
n
×ℙ
m
with values in various line bundles. Finally, we apply our method to developing weighted Koppelman formulas on Stein manifolds. 相似文献
3.
Symplectic instanton vector bundles on the projective space ℙ3 constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space I n;r of rank-2r symplectic instanton vector bundles on ℙ3 with r ≥ 2 and second Chern class n ≥ r, n ≡ r (mod 2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus I n;r * of tame symplectic instantons is irreducible and has the expected dimension, equal to 4n(r + 1) −r(2r + 1). 相似文献
4.
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line ℂ, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing
new asymptotic invariants. We show that the underlying holomorphic bundle extends to T×ℙ1. The converse statement is also true, namely a holomorphic bundle on T×ℙ1 which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton. Finally,
we study the hyperk?hler geometry of the moduli space of doubly-periodic instantons, and prove that the Nahm transform previously
defined by the second author is a hyperk?hler isometry with the moduli space of certain meromorphic Higgs bundles on the dual
torus.
Received June 8, 2000 / final version received February 1, 2001?Published online April 3, 2001 相似文献
5.
LetV ⊂ ℙℝ
n
be an algebraic variety, such that its complexificationV
ℂ ⊂ ℙ
n
is irreducible of codimensionm ≥ 1. We use a sufficient condition on a linear spaceL ⊂ ℙℝ
n
of dimensionm + 2r to have a nonempty intersection withV, to show that any six dimensional subspace of 5 × 5 real symmetric matrices contains a nonzero matrix of rank at most 3. 相似文献
6.
Mirella Manaresi 《manuscripta mathematica》1990,69(1):133-151
Stromme (see [S], (1.7)) introduced the notion of jumping conic of a normalized semistable rank two vector bundle E on ℙ2 and he remarked that the locus of jumping conics of E has codimension ≤3+2c1(E), with equality for general E.
Here we introduce a concept of jumping conic of a semistable rank two vector bundle on ℙ2 (see (I.1)) by generalizing the notion of jumping line of the second kind introduced by Hulek in [H]. Our definition agrees
with Stromme's for c1=−1, but not for c1=0. In contrast with the case of jumping lines, where we have a different behaviour in the case c1 even or c1 odd, the set of jumping conics according to our definition is always a divisor (possibly empty) in the ℙ5 of all conics of ℙ2 (see th. (I.8)), whose degree depends on c2(E). 相似文献
7.
Romain Dujardin 《Mathematische Annalen》2003,325(4):745-765
In this paper we study laminar currents in ℙ2. Given a sequence of irreducible algebraic curves (C
n
) converging in the sense of currents to T, we find geometric conditions on the curves ensuring that the limit current T is laminar. This criterion is then applied to meromorphic dynamical systems in ℙ2, and laminarity of the dynamical ``Green' current is obtained for a wide class of meromorphic self maps of ℙ2, as well as for all bimeromorphic maps of projective surfaces.
Received: 24 September 2001 / Published online: 10 February 2003
Mathematics Subject Classification (2000): 32U40, 37Fxx, 32H50 相似文献
8.
Burkhard Wilking 《Inventiones Mathematicae》2001,144(2):281-295
The diameter rigidity theorem of Gromoll and Grove [1987] states that a Riemannian manifold with sectional curvature ≥ 1 and
diameter ≥ π/2 is either homeomorphic to a sphere, locally isometric to a rank one symmetric space, or it has the cohomology
ring of the Cayley plane Caℙ. The reason that they were only able to recognize the cohomology ring of Caℙ is due to an exceptional
case in another theorem [Gromoll and Grove, 1988]: A Riemannian submersion σ:?m→B
b with connected fibers that is defined on the Euclidean sphere ?m is metrically congruent to a Hopf fibration unless possibly (m,b)=(15,8). We will rule out the exceptional cases in both theorems. Our argument relies on a rather unusal application of Morse
theory. For that purpose we give a general criterion which allows to decide whether the Morse index of a closed geodesic is
even or odd.
Oblatum 7-II-2000 & 11-X-2000?Published online: 29 January 2001 相似文献
9.
André Meireles Fernando Xavier Jacqueline Rojas 《Bulletin of the Brazilian Mathematical Society》2010,41(4):531-550
Here we construct an explicit parameter space for cones in ℙ
n
for 4 ≤ n ≤ 6 with vertices of codimension 4 and 5, respectively (when this makes sense), over a reducible cubic scroll of codimension
2 in a hyperplane (in ℙ
n
) and use it to compute the numbers of them that are incident to the appropriate number of linear spaces. 相似文献
10.
Carla Dionisi 《Annali di Matematica Pura ed Applicata》1998,175(1):285-293
Let
be the moduli space of stable symplectic instanton bundles on 2n+1 with second Chern class c2=k (it is a closed subscheme of the moduli space
).We prove that the dimension of its Zariski tangent space at a special (symplectic) instanton bundle is 2k(5n–1)+4n2–10n+3, k2. 相似文献
11.
In this paper we prove that, for anyn≥3, there exist infinitely manyr∈N and for each of them a smooth, connected curveC
r in ℙ
r
such thatC
r lies on exactlyn irreducible components of the Hilbert scheme Hilb(ℙ
r
). This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type. 相似文献
12.
The maximal Seshadri number μ(L) of an ample line bundle L on a smooth projective variety X measures the local positivity of the line bundle L at a general point of X. By refining the method of Ein-Küchle-Lazarsfeld, lower bounds on μ(L) are obtained in terms of L
n
, n=dim(X), for a class of varieties. The main idea is to show that if a certain lower bound is violated, there exists a non-trivial
foliation on the variety whose leaves are covered by special curves. In a number of examples, one can show that such foliations
must be trivial and obtain lower bounds for μ(L). The examples include the hyperplane line bundle on a smooth surface in ℙ3 and ample line bundles on smooth threefolds of Picard number 1.
Received: 29 June 2001 / Published online: 16 October 2002
RID="⋆"
ID="⋆" Supported by Grant No. 98-0701-01-5-L from the KOSEF.
RID="⋆⋆"
ID="⋆⋆" Supported by Grant No. KRF-2001-041-D00025 from the KRF. 相似文献
13.
Mirella Manaresi 《Geometriae Dedicata》1989,31(1):1-17
We study a class of ruled threefolds, namely, manifolds X with a projection p:X→ℙ2, such that each fiber is isomorphic to ℙ1, and which are homeomorphic to ℙ2×ℙ1; and we characterize ample and very ample line bundles on such threefolds.
This paper was written with the financial support of M.P.I. The author is a member of G.N.S.A.G.A. of the C.N.R. 相似文献
14.
Pietro De Poi 《manuscripta mathematica》2001,106(1):101-116
We discuss projective families of lines of ℙ
n
, and in particular congruences of order one. After giving general results, we obtain a complete classification of the case
of ℙ4 in which there is a fundamental curve.
Received: 2 August 2000 / Revised version: 11 July 2001 相似文献
15.
In this note we are interested in the graded modulesM
k=I(k)/Ik and
, whereI is a saturated ideal in the homogeneous coordinate ringS=K[x0,…,xn] of ℙn,I
(k) is the symbolic power and
is the saturation of the ordinary power. Very little is known about these modules, and we provide a bound on their diameters,
we compute the Hilbert functions and we study some characteristic submodules in the special case ofn+1 general points in ℙn.
Sunto In questa nota siamo interessati ai moduli graduatiM k=I(k)/Ik e , doveI è un ideale saturato nell'anello delle coordinate omogeneeS:=K[x0,…,xn] di ℙn,I (k) è la potenza simbolica e è la saturazione della potenza ordinaria. Poco è noto su questi moduli e qui viene fornito un limite superiore ai loro diametri. Ne calcoliamo inoltre le funzioni di Hilbert e studiamo alcuni sottomoduli caratteristici nel caso speciale din+1 punti in posizione generale, in ℙn.相似文献
16.
A 2 - (υ, k, 1) design D = (ℙ,ℙ, ℬ) is a system consisting of a finite set ℙ of υ points and a collection ℬ of ℙ-subsets of ℙ, called blocks, such
that each 2-subset of ℙ is contained in precisely one block. Let G be an automorphism group of a 2-(υ, k, 1) design. Delandtsheer proved that if G is block-primitive and D is not a projective plane, then G is almost simple, that is, T ⩽ G ⩽ Aut(T), where T is a non-abelian simple group. In this paper, we prove that T is not isomorphic to 3
D
4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design. 相似文献
17.
Let G be a discrete subgroup of PU(1,n). Then G acts on ℙℂ
n
preserving the unit ball ℍℂ
n
, where it acts by isometries with respect to the Bergman metric. In this work we look at its action on all of ℙℂ
n
and determine its equicontinuity region Eq(G). This turns out to be the complement of the union of all complex projective hyperplanes in ℙℂ
n
which are tangent to ∂ℍℂ
n
at points in the Chen-Greenberg limit set Λ(G), a closed G-invariant subset of ∂ℍℂ
n
which is minimal for non-elementary groups. We also prove that the action on Eq(G) is discontinuous. Also , if the limit set is “sufficiently general” (i.e. it is not contained in any proper
k
-chain), then each connected component of Eq(G) is a holomorphy domain and it is a complete Kobayashi hyperbolic space. 相似文献
18.
Let ƒ be a polynomial automorphism of ℂk of degree λ, whose rational extension to ℙk maps the hyperplane at infinity to a single point. Given any positive closed current S on ℙk of bidegree (1,1), we show that the sequence λ−n(ƒn)*S converges in the sense of currents on ℙk to a linear combination of the Green current T+ of ƒ and the current of integration along the hyperplane at infinity. We give an interpretation of the coefficients in terms
of generalized Lelong numbers with respect to an invariant dynamical current for ƒ−1. 相似文献
19.
Minimal, rigid foliations by curves on ℂℙ
n 总被引:1,自引:0,他引:1
We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space ℂℙ
n
for every dimension n≥2 and every degree d≥2. Precisely, we construct a foliation ℱ which is induced by a homogeneous vector field of degree d, has a finite singular set and all the regular leaves are dense in the whole of ℂℙ
n
. Moreover, ℱ satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if
ℱ is conjugate to another holomorphic foliation by a homeomorphism sufficiently close to the identity, then these foliations
are also conjugate by a projective transformation. Finally, all these properties are persistent for small perturbations of
ℱ.?This is done by considering pseudo-groups generated on the unit ball 𝔹
n
⊆ℂ
n
by small perturbations of elements in Diff(ℂ
n
,0). Under open conditions on the generators, we prove the existence of many pseudo-flows in their closure (for the C
0-topology) acting transitively on the ball. Dynamical features as minimality, ergodicity, positive entropy and rigidity may
easily be derived from this approach. Finally, some of these pseudo-groups are realized in the transverse dynamics of polynomial
vector fields in ℂℙ
n
.
Received March 7, 2002 / final version received November 26, 2002?Published online February 7, 2003
Most of this work has been carried out during a visit of the first author to IMPA/RJ and a visit of the second author to the
University of Lille 1. We would like to thank these institutes for hospitality and express our gratitude to CNPq-Brazil and
CNRS-France for the financial support which made these visits possible. We are also indebted to Paulo Sad, Marcel Nicolau
and the referee whose comments helped us to improve on the preliminary version. Finally, the second author has partially conducted
this research for the Clay Mathematics Institute. 相似文献
20.
Mohamed Hmissi 《manuscripta mathematica》1992,75(1):293-302
Let ℙ=(P
t
)
t<0
be a semigroup of kernel and letm be an excessive reference measure for ℙ. In this work we prove that ℙ ism-basic if and only if everym.a.e. finite purely excessive function is represented by a unique exit law for ℙ. In this case we deduce some applications
about natural densities, energie functionnal and invariant functions for the time-space semigroup of ℙ.
相似文献