The existence of equivariant pure free resolutions
David Eisenbud[1]; Gunnar Fløystad[2]; Jerzy Weyman[3]
- [1] Dept of Mathematics Berkeley, CA 94720 (USA)
- [2] Matematisk Institutt Johs. Brunsgt. 12 5008 Bergen (Norway)
- [3] Northeastern University Department of Mathematics 360 Huntington Avenue Boston, MA 02115 (USA)
Annales de l’institut Fourier (2011)
- Volume: 61, Issue: 3, page 905-926
- ISSN: 0373-0956
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topEisenbud, David, Fløystad, Gunnar, and Weyman, Jerzy. "The existence of equivariant pure free resolutions." Annales de l’institut Fourier 61.3 (2011): 905-926. <http://eudml.org/doc/219721>.
@article{Eisenbud2011,
abstract = {Let $A=K[x_1,\dots , x_m]$ be a polynomial ring in $m$ variables and let $\{\bf d\}=(d_0<\cdots < d_m)$ be a strictly increasing sequence of $m+1$ integers. Boij and Söderberg conjectured the existence of graded $A$-modules $M$ of finite length having pure free resolution of type $\mathbf\{d\}$ in the sense that for $i=0,\dots ,m$ the $i$-th syzygy module of $M$ has generators only in degree $d_i$.This paper provides a construction, in characteristic zero, of modules with this property that are also $GL(m)$-equivariant. Moreover, the construction works over rings of the form $A\otimes _K B$ where $A$ is a polynomial ring as above and $B$ is an exterior algebra.},
affiliation = {Dept of Mathematics Berkeley, CA 94720 (USA); Matematisk Institutt Johs. Brunsgt. 12 5008 Bergen (Norway); Northeastern University Department of Mathematics 360 Huntington Avenue Boston, MA 02115 (USA)},
author = {Eisenbud, David, Fløystad, Gunnar, Weyman, Jerzy},
journal = {Annales de l’institut Fourier},
keywords = {Pure resolution; equivariant resolution; Betti diagram; Boij-Söderberg theory; Pieri map; determinantal variety; pure resolution},
language = {eng},
number = {3},
pages = {905-926},
publisher = {Association des Annales de l’institut Fourier},
title = {The existence of equivariant pure free resolutions},
url = {http://eudml.org/doc/219721},
volume = {61},
year = {2011},
}
TY - JOUR
AU - Eisenbud, David
AU - Fløystad, Gunnar
AU - Weyman, Jerzy
TI - The existence of equivariant pure free resolutions
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 3
SP - 905
EP - 926
AB - Let $A=K[x_1,\dots , x_m]$ be a polynomial ring in $m$ variables and let ${\bf d}=(d_0<\cdots < d_m)$ be a strictly increasing sequence of $m+1$ integers. Boij and Söderberg conjectured the existence of graded $A$-modules $M$ of finite length having pure free resolution of type $\mathbf{d}$ in the sense that for $i=0,\dots ,m$ the $i$-th syzygy module of $M$ has generators only in degree $d_i$.This paper provides a construction, in characteristic zero, of modules with this property that are also $GL(m)$-equivariant. Moreover, the construction works over rings of the form $A\otimes _K B$ where $A$ is a polynomial ring as above and $B$ is an exterior algebra.
LA - eng
KW - Pure resolution; equivariant resolution; Betti diagram; Boij-Söderberg theory; Pieri map; determinantal variety; pure resolution
UR - http://eudml.org/doc/219721
ER -
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