共查询到20条相似文献,搜索用时 15 毫秒
1.
We determine which singular del Pezzo surfaces are equivariant compactifications of
\mathbbG\texta2 \mathbb{G}_{\text{a}}^2 , to assist with proofs of Manin’s conjecture for such surfaces. Additionally, we give an example of a singular quartic del
Pezzo surface that is an equivariant compactification of
\mathbbG\texta {\mathbb{G}_{\text{a}}} ⋊
\mathbbG\textm {\mathbb{G}_{\text{m}}} . Bibliography: 32 titles. 相似文献
2.
Let μ be a Poisson random measure, let
\mathbbF\mathbb{F} be the smallest filtration satisfying the usual conditions and containing the one generated by μ, and let
\mathbbG\mathbb{G} be the initial enlargement of
\mathbbF\mathbb{F} with the σ-field generated by a random variable G. In this paper, we first show that the mutual information between the enlarging random variable G and the σ-algebra generated by the Poisson random measure μ is equal to the expected relative entropy of the
\mathbbG\mathbb{G}-compensator relative to the
\mathbbF\mathbb{F}-compensator of the random measure μ. We then use this link to gain some insight into the changes of Doob–Meyer decompositions of stochastic processes when the
filtration is enlarged from
\mathbbF\mathbb{F} to
\mathbbG\mathbb{G}. In particular, we show that if the mutual information between G and the σ-algebra generated by the Poisson random measure μ is finite, then every square-integrable
\mathbbF\mathbb{F}-martingale is a
\mathbbG\mathbb{G}-semimartingale that belongs to the normed space S1\mathcal{S}^{1} relative to
\mathbbG\mathbb{G}. 相似文献
3.
The motivation for this paper comes from the Halperin–Carlsson conjecture for (real) moment-angle complexes. We first give
an algebraic combinatorics formula for the M?bius transform of an abstract simplicial complex K on [m]={1,…,m} in terms of the Betti numbers of the Stanley–Reisner face ring k(K) of K over a field k. We then employ a way of compressing K to provide the lower bound on the sum of those Betti numbers using our formula. Next we consider a class of generalized moment-angle
complexes
ZK(\mathbb D, \mathbb S)\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})}, including the moment-angle complex ZK\mathcal{Z}_{K} and the real moment-angle complex
\mathbbRZK\mathbb{R}\mathcal {Z}_{K} as special examples. We show that
H*(ZK(\mathbb D, \mathbb S);k)H^{*}(\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})};\mathbf{k}) has the same graded k-module structure as Tor
k[v](k(K),k). Finally we show that the Halperin–Carlsson conjecture holds for ZK\mathcal{Z}_{K} (resp.
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}) under the restriction of the natural T
m
-action on ZK\mathcal{Z}_{K} (resp. (ℤ2)
m
-action on
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}). 相似文献
4.
Alexander Premet 《Inventiones Mathematicae》2010,181(2):395-420
Let ${\mathfrak{g}}Let
\mathfrakg{\mathfrak{g}} be a finite dimensional simple Lie algebra over an algebraically closed field
\mathbbK\mathbb{K} of characteristic 0. Let
\mathfrakg\mathbbZ{\mathfrak{g}}_{{\mathbb{Z}}} be a Chevalley ℤ-form of
\mathfrakg{\mathfrak{g}} and
\mathfrakg\Bbbk=\mathfrakg\mathbbZ?\mathbbZ\Bbbk{\mathfrak{g}}_{\Bbbk}={\mathfrak{g}}_{{\mathbb{Z}}}\otimes _{{\mathbb{Z}}}\Bbbk, where
\Bbbk\Bbbk is the algebraic closure of
\mathbbFp{\mathbb{F}}_{p}. Let
G\BbbkG_{\Bbbk} be a simple, simply connected algebraic
\Bbbk\Bbbk-group with
\operatornameLie(G\Bbbk)=\mathfrakg\Bbbk\operatorname{Lie}(G_{\Bbbk})={\mathfrak{g}}_{\Bbbk}. In this paper, we apply recent results of Rudolf Tange on the fraction field of the centre of the universal enveloping algebra
U(\mathfrakg\Bbbk)U({\mathfrak{g}}_{\Bbbk}) to show that if the Gelfand–Kirillov conjecture (from 1966) holds for
\mathfrakg{\mathfrak{g}}, then for all p≫0 the field of rational functions
\Bbbk (\mathfrakg\Bbbk)\Bbbk ({\mathfrak{g}}_{\Bbbk}) is purely transcendental over its subfield
\Bbbk(\mathfrakg\Bbbk)G\Bbbk\Bbbk({\mathfrak{g}}_{\Bbbk})^{G_{\Bbbk}}. Very recently, it was proved by Colliot-Thélène, Kunyavskiĭ, Popov, and Reichstein that the field of rational functions
\mathbbK(\mathfrakg){\mathbb{K}}({\mathfrak{g}}) is not purely transcendental over its subfield
\mathbbK(\mathfrakg)\mathfrakg{\mathbb{K}}({\mathfrak{g}})^{\mathfrak{g}} if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4. We prove a modular version of this result (valid for p≫0) and use it to show that, in characteristic 0, the Gelfand–Kirillov conjecture fails for the simple Lie algebras of the
above types. In other words, if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4, then the Lie field of
\mathfrakg{\mathfrak{g}} is more complicated than expected. 相似文献
5.
Let
\mathbbF\mathbb{F} be a field of characteristic 0, and let G be an additive subgroup of
\mathbbF\mathbb{F}. We define a class of infinite-dimensional Lie algebras
\mathbbF\mathbb{F}-basis {L
μ, V
μ, W
μ | μ ∈ G}, which are very closely related to W-algebras. In this paper, the second cohomology group of is determined. 相似文献
6.
Shikun OU 《Frontiers of Mathematics in China》2012,7(3):497-512
Let F be a field, and let
\mathbbG\mathbb{G} be the standard Borel subgroup of the symplectic group Sp(2m, F). In this paper, we characterize the bijective maps ϕ:
\mathbbG\mathbb{G} →
\mathbbG\mathbb{G} satisfying ϕ[x, y] = [ϕ(x), ϕ(y)]. 相似文献
7.
We study the limiting behavior of the K?hler–Ricci flow on
\mathbbP(O\mathbbPn ?O\mathbbPn(-1)?(m+1)){{\mathbb{P}(\mathcal{O}_{\mathbb{P}^n} \oplus \mathcal{O}_{\mathbb{P}^n}(-1)^{\oplus(m+1)})}} for m, n ≥ 1, assuming the initial metric satisfies the Calabi symmetry. We show that the flow either shrinks to a point, collapses
to
\mathbbPn{{\mathbb{P}^n}} or contracts a subvariety of codimension m + 1 in the Gromov–Hausdorff sense. We also show that the K?hler–Ricci flow resolves a certain type of cone singularities
in the Gromov–Hausdorff sense. 相似文献
8.
We prove a “unique crossed product decomposition” result for group measure space II1 factors L ∞(X)⋊Γ arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups Γ in a fairly large family
G\mathcal{G}, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products
over an amenable subgroup. We deduce that if T
n
denotes the group of upper triangular matrices in PSL (n,ℤ), then any free, mixing p.m.p. action of
G = \operatornamePSL(n,\mathbbZ)*Tn\operatornamePSL(n,\mathbbZ)\Gamma=\operatorname{PSL}(n,\mathbb{Z})*_{T_{n}}\operatorname{PSL}(n,\mathbb{Z}) is W∗-superrigid, i.e. any isomorphism between L ∞(X)⋊Γ and an arbitrary group measure space factor L ∞(Y)⋊Λ, comes from a conjugacy of the actions. We also prove that for many groups Γ in the family G\mathcal{G}, the Bernoulli actions of Γ are W∗-superrigid. 相似文献
9.
A. S. Morozov 《Algebra and Logic》2012,51(1):66-88
It is proved that every two Σ-presentations of an ordered field \mathbbR \mathbb{R} of reals over \mathbbH\mathbbF ( \mathbbR ) \mathbb{H}\mathbb{F}\,\left( \mathbb{R} \right) , whose universes are subsets of \mathbbR \mathbb{R} , are mutually Σ-isomorphic. As a consequence, for a series of functions f:\mathbbR ? \mathbbR f:\mathbb{R} \to \mathbb{R} (e.g., exp, sin, cos, ln), it is stated that the structure \mathbbR \mathbb{R} = 〈R, +, ×, <, 0, 1, f〉 lacks such Σ-presentations over \mathbbH\mathbbF ( \mathbbR ) \mathbb{H}\mathbb{F}\,\left( \mathbb{R} \right) . 相似文献
10.
D. V. Millionshchikov 《Mathematical Notes》2005,77(1):61-71
The cohomology H
\mathfrakg\mathfrak{g}
) of the tangent Lie algebra
\mathfrakg\mathfrak{g}
of the group G with coefficients in the one-dimensional representation
\mathfrakg\mathfrak{g}
\mathbbK\mathbb{K}
defined by
[(W)\tilde] \mathfrakg \tilde \Omega _\mathfrak{g}
of H
1(G/
\mathfrakg\mathfrak{g}
. 相似文献
11.
Let G be a finite non-Abelian group. We define a graph Γ
G
; called the noncommuting graph of G; with a vertex set G − Z(G) such that two vertices x and y are adjacent if and only if xy ≠ yx: Abdollahi, Akbari, and Maimani put forward the following conjecture (the AAM conjecture): If S is a finite non-Abelian simple group and G is a group such that Γ
S
≅ Γ
G
; then S ≅ G: It is still unknown if this conjecture holds for all simple finite groups with connected prime graph except
\mathbbA10 {\mathbb{A}_{10}} , L
4(8), L
4(4), and U
4(4). In this paper, we prove that if
\mathbbA16 {\mathbb{A}_{16}} denotes the alternating group of degree 16; then, for any finite group G; the graph isomorphism
G\mathbbA16 @ GG {\Gamma_{{\mathbb{A}_{16}}}} \cong {\Gamma_G} implies that
\mathbbA16 @ G {\mathbb{A}_{16}} \cong G . 相似文献
12.
John R. Akeroyd 《Arkiv f?r Matematik》2011,49(1):1-16
It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that
G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\}
and with the property that the analytic polynomials are dense in the Bergman space
\mathbbAt(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)
. It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous
real-valued function on [0,1], where the polynomials are dense in
Ht(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma)
; improving upon a result in an earlier paper. 相似文献
13.
Atsumu Sasaki 《Geometriae Dedicata》2010,145(1):151-158
Let G/K be an irreducible Hermitian symmetric space of non-compact type, and
G\mathbbC/K\mathbbC{G_{\mathbb{C}}/K_{\mathbb{C}}} its complexification by forgetting the original complex structure. Then,
D :=G\mathbbC/[K\mathbbC, K\mathbbC]{D :=G_{\mathbb{C}}/[K_{\mathbb{C}}, K_{\mathbb{C}}]} is a non-symmetric Stein manifold. We prove that a maximal compact subgroup of
G\mathbbC{G_{\mathbb{C}}} acts on D in a strongly visible fashion in the sense of Kobayashi (Publ Res Inst Math Sci 41:497–549, 2005) if and only if G/K is of non-tube type. Our proof uses the theory of multiplicity-free representations and a construction of a slice and an
anti-holomorphic involution on D. 相似文献
14.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
15.
We study hypersurfaces in the Lorentz-Minkowski space
\mathbbLn+1{\mathbb{L}^{n+1}} whose position vector ψ satisfies the condition L
k
ψ = Aψ + b, where L
k
is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed k = 0, . . . , n − 1,
A ? \mathbbR(n+1)×(n+1){A\in\mathbb{R}^{(n+1)\times(n+1)}} is a constant matrix and
b ? \mathbbLn+1{b\in\mathbb{L}^{n+1}} is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature, open pieces of totally umbilical hypersurfaces
\mathbbSn1(r){\mathbb{S}^n_1(r)} or
\mathbbHn(-r){\mathbb{H}^n(-r)}, and open pieces of generalized cylinders
\mathbbSm1(r)×\mathbbRn-m{\mathbb{S}^m_1(r)\times\mathbb{R}^{n-m}},
\mathbbHm(-r)×\mathbbRn-m{\mathbb{H}^m(-r)\times\mathbb{R}^{n-m}}, with k + 1 ≤ m ≤ n − 1, or
\mathbbLm×\mathbbSn-m(r){\mathbb{L}^m\times\mathbb{S}^{n-m}(r)}, with k + 1 ≤ n − m ≤ n − 1. This completely extends to the Lorentz-Minkowski space a previous classification for hypersurfaces in
\mathbbRn+1{\mathbb{R}^{n+1}} given by Alías and Gürbüz (Geom. Dedicata 121:113–127, 2006). 相似文献
16.
Juan A. Aledo Victorino Lozano José A. Pastor 《Mediterranean Journal of Mathematics》2010,7(3):263-270
We prove that the only compact surfaces of positive constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} (resp. positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}}) whose boundary Γ is contained in a slice of the ambient space and such that the surface intersects this slice at a constant
angle along Γ, are the pieces of a rotational complete surface. We also obtain some area estimates for surfaces of positive
constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} and positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}} whose boundary is contained in a slice of the ambient space. These estimates are optimal in the sense that if the bounds
are attained, the surface is again a piece of a rotational complete surface. 相似文献
17.
Harald Grobner 《Monatshefte für Mathematik》2010,139(1):335-340
Let
G/\mathbb Q{G/\mathbb Q} be the simple algebraic group Sp(n, 1) and G = G(N){\Gamma=\Gamma(N)} a principal congruence subgroup of level N ≥ 3. Denote by K a maximal compact subgroup of the real Lie group
G(\mathbb R){G(\mathbb R)} . Then a double quotient
G\G(\mathbb R)/K{\Gamma\backslash G(\mathbb R)/K} is called an arithmetically defined, quaternionic hyperbolic n-manifold. In this paper we give an explicit growth condition for the dimension of cuspidal cohomology
H2ncusp(G\G(\mathbb R)/K,E){H^{2n}_{cusp}(\Gamma\backslash G(\mathbb R)/K,E)} in terms of the underlying arithmetic structure of G and certain values of zeta-functions. These results rely on the work of Arakawa (Automorphic Forms of Several Variables:
Taniguchi Symposium, Katata, 1983, eds. I. Satake and Y. Morita (Birkh?user, Boston), pp. 1–48, 1984). 相似文献
18.
Carlson and Toledo conjectured that if an infinite group Γ is the fundamental group of a compact K?hler manifold, then virtually
H2(G, \mathbb R) 1 0{H^{2}(\Gamma, {\mathbb R}) \ne 0} . We assume that Γ admits an unbounded reductive rigid linear representation. This representation necessarily comes from
a complex variation of Hodge structure (
\mathbbC{\mathbb{C}} -VHS) on the K?hler manifold. We prove the conjecture under some assumption on the
\mathbbC{\mathbb{C}} -VHS. We also study some related geometric/topological properties of period domains associated to such a
\mathbbC{\mathbb{C}} -VHS. 相似文献
19.
Andrea Bonfiglioli 《Archiv der Mathematik》2009,93(3):277-286
Let ${\mathbb{G}}Let
\mathbbG{\mathbb{G}} be a Carnot group of step r and m generators and homogeneous dimension Q. Let
\mathbbFm,r{\mathbb{F}_{m,r}} denote the free Lie group of step r and m generators. Let also
p:\mathbbFm,r?\mathbbG{\pi:\mathbb{F}_{m,r}\to\mathbb{G}} be a lifting map. We show that any horizontally convex function u on
\mathbbG{\mathbb{G}} lifts to a horizontally convex function u°p{u\circ \pi} on
\mathbbFm,r{\mathbb{F}_{m,r}} (with respect to a suitable horizontal frame on
\mathbbFm,r{\mathbb{F}_{m,r}}). One of the main aims of the paper is to exhibit an example of a sub-Laplacian L=?j=1m Xj2{\mathcal{L}=\sum_{j=1}^m X_j^2} on a Carnot group of step two such that the relevant L{\mathcal{L}}-gauge function d (i.e., d
2-Q
is the fundamental solution for L{\mathcal{L}}) is not h-convex with respect to the horizontal frame {X
1, . . . , X
m
}. This gives a negative answer to a question posed in Danielli et al. (Commun. Anal. Geom. 11 (2003), 263–341). 相似文献
20.
Indranil Biswas 《Archiv der Mathematik》2005,84(1):38-45
Let EG be an algebraic principal G-bundle over
\mathbbC\mathbbPn ,\mathbb{C}\mathbb{P}^n , n
\mathbbC.\mathbb{C}. We prove that EG admits a reduction of structure group to a one-parameter subgroup of G if and only if
$
H^1 (\mathbb{C}\mathbb{P}^n ,{\text{ ad(}}E_G )( - k)) = 0
$
H^1 (\mathbb{C}\mathbb{P}^n ,{\text{ ad(}}E_G )( - k)) = 0
相似文献
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