scholarly journals A Presentation of the Kähler Differential Module for a Fat Point Scheme in ℙn1 × … × ℙnk

2018 ◽  
Vol 20 ◽  
pp. 01007
Author(s):  
Tran N. K. Linh ◽  
Elena Guardo ◽  
Long Le Ngoc
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Characteristic Zero ◽  
Differential Module ◽  
Fat Point ◽  
Point Scheme

Let 핐 be a fat point scheme in ℙn1 × … × ℙnk over a field K of characteristic zero. In this paper we introduce the multi-graded Kähler differential module for 핐 and we establish a short exact sequence of this module in terms of the thickening of 핐.

Fat Points in ℙ1× ℙ1and Their Hilbert Functions

2004 ◽  
Vol 56 (4) ◽  
pp. 716-741 ◽  
Author(s):  
Elena Guardo ◽  
Adam Van Tuyl
Keyword(s):  
Finite Number ◽  
Hilbert Function ◽  
Free Resolution ◽  
Hilbert Functions ◽  
Minimal Free Resolution ◽  
Fat Points ◽  
Fat Point ◽  
Point Scheme

AbstractWe study the Hilbert functions of fat points in ℙ1× ℙ1. IfZ⊆ ℙ1× ℙ1is an arbitrary fat point scheme, then it can be shown that for everyiandjthe values of the Hilbert functionHZ(l,j) andHZ(i,l) eventually become constant forl≫ 0. We show how to determine these eventual values by using only the multiplicities of the points, and the relative positions of the points in ℙ1× ℙ1. This enables us to compute all but a finite number values ofHZwithout using the coordinates of points. We also characterize the ACM fat point schemes using our description of the eventual behaviour. In fact, in the case thatZ⊆ ℙ1× ℙ1is ACM, then the entire Hilbert function and its minimal free resolution depend solely on knowing the eventual values of the Hilbert function.

scholarly journals Continuation homomorphism in Rabinowitz Floer homology for symplectic deformations

2011 ◽  
Vol 151 (3) ◽  
pp. 471-502 ◽  
Author(s):  
YOUNGJIN BAE ◽  
URS FRAUENFELDER
Keyword(s):  
Exact Sequence ◽  
Isoperimetric Inequality ◽  
Short Exact Sequence ◽  
Loop Space ◽  
Floer Homology ◽  
Critical Value ◽  
Alternative Proof ◽  
Rabinowitz Floer Homology ◽  
Space Homology ◽  
Loop Space Homology

AbstractWill J. Merry computed Rabinowitz Floer homology above Mañé's critical value in terms of loop space homology in [14] by establishing an Abbondandolo–Schwarz short exact sequence. The purpose of this paper is to provide an alternative proof of Merry's result. We construct a continuation homomorphism for symplectic deformations which enables us to reduce the computation to the untwisted case. Our construction takes advantage of a special version of the isoperimetric inequality which above Mañé's critical value holds true.

scholarly journals Group cohomology with coefficients in a crossed module

2010 ◽  
Vol 10 (2) ◽  
pp. 359-404 ◽  
Author(s):  
Behrang Noohi
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Geometric Approach ◽  
Group Cohomology ◽  
Theoretic Approach ◽  
Crossed Module ◽  
Explicit Approach ◽  
Crossed Modules ◽  
Cohomology Sequence

AbstractWe compare three different ways of defining group cohomology with coefficients in a crossed module: (1) explicit approach via cocycles; (2) geometric approach via gerbes; (3) group theoretic approach via butterflies. We discuss the case where the crossed module is braided and the case where the braiding is symmetric. We prove the functoriality of the cohomologies with respect to weak morphisms of crossed modules and also prove the ‘long’ exact cohomology sequence associated to a short exact sequence of crossed modules and weak morphisms.

Gelfand-Kirillov Dimension is Exact for Noetherian PI Algebras

1984 ◽  
Vol 27 (2) ◽  
pp. 247-250 ◽  
Author(s):  
T. H. Lenagan
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Finitely Generated ◽  
Finitely Generated Modules ◽  
Kirillov Dimension

AbstractIf O → A → C → B → O is a short exact sequence of finitely generated modules over a Noetherian Pi-algebra then we show that GK(C) = max{GK(A), GK(B)}.

scholarly journals Non-abelian exterior products of groups and exact sequences in the homology of groups

1987 ◽  
Vol 29 (1) ◽  
pp. 13-19 ◽  
Author(s):  
G. J. Ellis
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Type Theorem ◽  
Exterior Product ◽  
Products Of Groups ◽  
Hopf Formula ◽  
Definition Of ◽  
Image Position ◽  
Exact Sequences

Various authors have obtained an eight term exact sequence in homologyfrom a short exact sequence of groups,the term V varying from author to author (see [7] and [2]; see also [5] for the simpler case where N is central in G, and [6] for the case where N is central and N ⊂ [G, G]). The most satisfying version of the sequence is obtained by Brown and Loday [2] (full details of [2] are in [3]) as a corollary to their van Kampen type theorem for squares of spaces: they give the term V as the kernel of a map G ∧ N → N from a “non-abelian exterior product” of G and N to the group N (the definition of G ∧ N, first published in [2], is recalled below). The two short exact sequencesandwhere F is free, together with the fact that H2(F) = 0 and H3(F) = 0, imply isomorphisms..The isomorphism (2) is essentially the description of H2(G) proved algebraically in [11]. As noted in [2], the isomorphism (3) is the analogue for H3(G) of the Hopf formula for H2(G).

The Nature of Short Exact Sequence

2020 ◽  
Vol 10 (08) ◽  
pp. 719-725
Author(s):  
宏涛 范
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence

scholarly journals Equivariant splitting of the Hodge–de Rham exact sequence

2021 ◽  
Author(s):  
Jędrzej Garnek
Keyword(s):  
Finite Group ◽  
Exact Sequence ◽  
Short Exact Sequence ◽  
Algebraic Curve ◽  
Hyperelliptic Curves ◽  
Witt Vectors ◽  
De Rham ◽  
A Finite Group

AbstractLet X be an algebraic curve with a faithful action of a finite group G over a field k. We show that if the Hodge–de Rham short exact sequence of X splits G-equivariantly then the action of G on X is weakly ramified. In particular, this generalizes the result of Köck and Tait for hyperelliptic curves. We discuss also converse statements and tie this problem to lifting coverings of curves to the ring of Witt vectors of length 2.

scholarly journals The tracial topological rank of extensions of $C^*$-algebras

2004 ◽  
Vol 94 (1) ◽  
pp. 125 ◽  
Author(s):  
Shanwen Hu ◽  
Huaxin Lin ◽  
Yifeng Xue
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Rank Zero ◽  
C Algebras ◽  
Tracial Topological Rank ◽  
Quasidiagonal Extension

Let $0\to \mathcal J\to \mathcal A\to \mathcal A / \mathcal J\to 0$ be a short exact sequence of separable $C^*$-algebras. We introduce the notion of tracially quasidiagonal extension. Suppose that $\mathcal J$ and $\mathcal A/J$ have tracial topological rank zero. We prove that if $(\mathcal A, \mathcal J)$ is tracially quasidiagonal, then $\mathcal A$ has tracial topological rank zero.

Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories

2020 ◽  
Vol 48 (6) ◽  
pp. 2639-2654
Author(s):  
Septimiu Crivei ◽  
Derya Keskin Tütüncü ◽  
Rachid Tribak
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Abelian Categories

Tracially Quasidiagonal Extensions

2003 ◽  
Vol 46 (3) ◽  
pp. 388-399 ◽  
Author(s):  
Huaxin Lin
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Tracial Topological Rank ◽  
Unital Simple ◽  
Quasidiagonal Extension

AbstractIt is known that a unital simple C*-algebra A with tracial topological rank zero has real rank zero. We show in this note that, in general, there are unital C*-algebras with tracial topological rank zero that have real rank other than zero.Let 0 → J → E → A → 0 be a short exact sequence of C*-algebras. Suppose that J and A have tracial topological rank zero. It is known that E has tracial topological rank zero as a C*-algebra if and only if E is tracially quasidiagonal as an extension. We present an example of a tracially quasidiagonal extension which is not quasidiagonal.

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