共查询到20条相似文献,搜索用时 0 毫秒
1.
We describe the algebras of semi-invariants on the varieties of regular representations of canonical algebras. In particular,
we show that these algebras are polynomial algebras or complete intersections.
Received: 29 March 1999 相似文献
2.
Tyler J. Jarvis 《Mathematische Zeitschrift》2000,235(1):123-149
This article provides two different, but closely related, moduli problems, which in characteristic zero provide a type of
compactification of the universal Picard over the moduli of stable curves. Although neither is of finite type, both are limits
of a sequence of stacks, each of which is a separated algebraic stack of finite type. We discuss relations to previous compactifications
and partial compactifications, give a number of examples related to this compactification, and work out the structure of its
fibres over certain fixed curves. Some applications are also discussed.
Received January 5, 1998; in final form April 1, 1999 / Published online July 3, 2000 相似文献
3.
Let B be a block of the group algebra KG of a finite Group G over an algebraically closed field K. We prove that every degeneration of finite dimensional B-modules is given by short exact sequences if and only if B is of finite representation type.
Received: 7 July 1997 相似文献
4.
Dmitri I. Panyushev 《manuscripta mathematica》1999,99(2):185-202
Let G be a reductive algebraic group and X a smooth G-variety. For a smooth locally closed G-stable subvariety M⊂X, we prove that the G-complexity of the (co)normal bundle of M is equal to the G-complexity of X. In particular, if X is spherical, then all (co)normal bundles are again spherical G-varieties. If X is a G-module with finitely many orbits, the closures of the conormal bundles of the orbits coincide with the irreducible components
of the commuting variety. We describe properties of these closures for the representations associated with short gradings
of simple Lie algebras.
Received: 22 April 1998 相似文献
5.
Jin-Xing Cai 《Mathematische Zeitschrift》2002,240(3):511-519
Received: 15 October 1999; in final form: 13 June 2000 / Published online: 29 April 2002 相似文献
6.
We study the slopes of Frobenius on the rigid cohomology and the rigid cohomology with compact support of an algebraic variety over a perfect field of positive characteristic. We then prove that any unipotent overconvergent F-isocrystal on a smooth variety has a slope filtration whose graded parts are pure. Received: 23 December 1998 / Revised version: 5 July 1999 相似文献
7.
Using descent theory, we study Hopf algebra forms of pointed Hopf algebras. It turns out that the set of isomorphism classes
of such forms are in one-to-one correspondence to other known invariants, for example the set of isomorphism classes of Galois
extensions with a certain group F, or the set of isometry classes of m-ary quadratic forms. Our theory leads to a classification of all Hopf algebras over a field of characteristic zero that become
pointed after a base extension, in dimension p, p
2 and p
3, with p odd.
Received: 22 November 1998 相似文献
8.
Fabien Trihan 《manuscripta mathematica》1998,96(4):397-419
The purpose of this article is to give a cohomological formula for the unit-root part of the L-function associated to a Barsotti-Tate group G on a scheme S over a field of characteristic p when G extends to some compactification of S. This is an analogue of a part of a conjecture of Katz according to wich the L-function of an F-crystal should be expressed in terms of the p-adic etale sheaf corresponding to the unit-root part of the crystal. In order to carry out this project, we use the technics
of [E-LS II] wich require in our case an extension of the Dieudonné crystalline theory ([B-B-M]) to “crystal of level mG” in the sense of Berthelot. We show that the unit-root L-function of the Dieudonné crystal associated to G can be expressed in terms of the syntomic cohomology of the Ext group of G by the constant sheaf.
Received: 24 March 1997 / Revised version: 6 January 1998 相似文献
9.
10.
11.
It is known that the orbit closures for the representations of the equioriented Dynkin quivers ? n are normal and Cohen–Macaulay varieties with rational singularities. In the paper we prove the same for the Dynkin quivers ? n with arbitrary orientation. Received: 25 October 2000 / Revised version: 28 February 2001 相似文献
12.
Martin R. Bridson 《Mathematische Annalen》2000,317(4):629-633
Abstract. We construct finitely presented subgroups of GL that have infinitely many conjugacy classes of finite subgroups. This answers a question of Grunewald and Platonov. We suggest
a variation on their question.
Received: 26 August 1999 / Revised: 28 September 1999 / Published online: 8 May 2000 相似文献
13.
Giovanni Gaiffi 《manuscripta mathematica》1998,97(3):353-369
Let be the complexified Coxeter arrangement of hyperplanes of type A
n
−1 (n≥ 3). It is well known that the “minimal” projective De Concini–Procesi model of is isomorphic to the moduli space of stable n plus;1-pointed curves of genus 0. In this paper we study, from the point of view of models of arrangements, the action of
the symmetric group Σ
n
on the integer cohomology ring of . In fact we find a formula for the generalized Poincaré series which
encodes all the information about this representation of Σ
n
. This formula, which is obtained by using the elementary combinatorial properties of a ℤ-basis of and turns out to be very direct, should be compared with a more general result due to Getzler (see [5]).
Received: 24 November 1997 / Revised version: 23 April 1998 相似文献
14.
Jörg Jahnel 《manuscripta mathematica》1998,96(4):421-442
Let X be an arithmetic variety and L be an element of the Néron-Severi group of its generic fiber X
K
. Then there are only finitely many line bundles on X, generically belonging to L, such that the degrees of on the irreducible components of the special fibers of X and the height of are bounded. The concept of a height used here is recalled. Several elementary properties of this height are proven.
Received: 9 March 1996 相似文献
15.
We discuss a technique for trying to find all rational points on curves of the form Y
2=f
3
X
6+f
2
X
4+f
1
X
2+f
0, where the sextic has nonzero discriminant. This is a bielliptic curve of genus 2. When the rank of the Jacobian is 0 or
1, Chabauty's Theorem may be applied. However, we shall concentrate on the situation when the rank is at least 2. In this
case, we shall derive an associated family of elliptic curves, defined over a number field ℚα. If each of these elliptic
curves has rank less than the degree of ℚα :
ℚ, then we shall describe a Chabauty-like technique which may be applied to try to find all the points (x,y) defined over ℚα) on the elliptic curves, for which x∈ℚ. This in turn allows us to find all ℚ-rational points on the original genus 2 curve. We apply this to give a solution to
a problem of Diophantus (where the sextic in X is irreducible over ℚ), which simplifies the recent solution of Wetherell. We also present two examples where the sextic
in X is reducible over ℚ.
Received: 27 November 1998 / Revised version: 4 June 1999 相似文献
16.
Alessandra Bertapelle 《Mathematische Annalen》2000,316(3):437-463
17.
Let D be the open unit ball of a -triple A and let Aut(D) be the group of all biholomorphic automorphisms of D. It is shown that every element of Aut(D) is sequentially weakly continuous if and only if every primitive ideal of A is a maximal closed ideal and is a type I -triple without infinite-spin part. Implications for general structure theory are explored. In particular, it is deduced that
every -triple A contains a smallest ideal J for which the sequentially weakly continuous biholomorphic automorphisms of the open unit ball of A/J are all linear.
Received August 27, 1998; in final form February 10, 1999 相似文献
18.
19.
Ronald Stöver 《Numerische Mathematik》2001,88(4):771-795
Summary. We consider boundary value problems for linear differential-algebraic equations with variable coefficients with no restriction on the index. A well-known regularisation procedure yields an equivalent index one problem with d differential and a=n-d algebraic equations. Collocation methods based on the regularised BVP approximate the solution x by a continuous piecewise polynomial of degree k and deliver, in particular, consistent approximations at mesh points by using the Radau schemes. Under weak assumptions, the collocation problems are uniquely and stably solvable and, if the unique solution x is sufficiently smooth, convergence of order min {k+1,2k-1} and superconvergence at mesh points of order 2k-1 is shown. Finally, some numerical experiments illustrating these results are presented. Received October 1, 1999 / Revised version received April 25, 2000 / Published online December 19, 2000 相似文献
20.
Summary. We present symmetric collocation methods for linear differential-algebraic boundary value problems without restrictions on
the index or the structure of the differential-algebraic equation. In particular, we do not require a separation into differential
and algebraic solution components. Instead, we use the splitting into differential and algebraic equations (which arises naturally
by index reduction techniques) and apply Gau?-type (for the differential part) and Lobatto-type (for the algebraic part) collocation
schemes to obtain a symmetric method which guarantees consistent approximations at the mesh points. Under standard assumptions,
we show solvability and stability of the discrete problem and determine its order of convergence. Moreover, we show superconvergence
when using the combination of Gau? and Lobatto schemes and discuss the application of interpolation to reduce the number of
function evaluations. Finally, we present some numerical comparisons to show the reliability and efficiency of the new methods.
Received September 22, 2000 / Revised version received February 7, 2001 / Published online August 17, 2001 相似文献