## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Computational Commutative Algebra and Combinatorics, T. Hibi, ed. (Tokyo: Mathematical Society of Japan, 2002), 53 - 64

### Algebraic Shifting and Spectral Sequences

#### Abstract

There is a canonical spectral sequence associated to any filtration of simplicial complexes. Algebraically shifting a finite filtration of simplicial complexes produces a new filtration of shifted complexes.

We prove that certain sums of the dimensions of the limit terms of the spectral sequence of a filtration weakly decrease by algebraically shifting the filtration. A key step is the combinatorial interpretation of the dimensions of the limit terms of the spectral sequence of a filtration consisting of near-cones.

#### Article information

**Source***Computational Commutative Algebra and Combinatorics*, T. Hibi, ed. (Tokyo: Mathematical Society of Japan, 2002), 53-64

**Dates**

Received: 29 May 2000

First available in Project Euclid:
31 December 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1546230152

**Digital Object Identifier**

doi:10.2969/aspm/03310053

**Mathematical Reviews number (MathSciNet)**

MR1890095

**Zentralblatt MATH identifier**

1022.55013

**Subjects**

Primary: 55T05: General

Secondary: 05A20: Combinatorial inequalities 05E99: None of the above, but in this section 52B05: Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx] 55N99: None of the above, but in this section

#### Citation

Duval, Art M. Algebraic Shifting and Spectral Sequences. Computational Commutative Algebra and Combinatorics, 53--64, Mathematical Society of Japan, Tokyo, Japan, 2002. doi:10.2969/aspm/03310053. https://projecteuclid.org/euclid.aspm/1546230152