A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Guralnick, Robert, and Tiep, Pham. "A problem of Kollár and Larsen on finite linear groups and crepant resolutions." Journal of the European Mathematical Society 014.3 (2012): 605-657. <http://eudml.org/doc/277416>.

@article{Guralnick2012,
abstract = {The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age $\le 1$. More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation. As a consequence of our main results, we derive some properties of symmetric spaces $GU_d(\mathbb \{C\})/G$ having shortest closed geodesics of bounded length, and of quotients $\mathbb \{C\}^d/G$ having a crepant resolution.},
author = {Guralnick, Robert, Tiep, Pham},
journal = {Journal of the European Mathematical Society},
keywords = {age; deviation; finite linear groups; complex reflection groups; crepant resolutions; quotient; finite linear group; complex reflection group; quotient},
language = {eng},
number = {3},
pages = {605-657},
publisher = {European Mathematical Society Publishing House},
title = {A problem of Kollár and Larsen on finite linear groups and crepant resolutions},
url = {http://eudml.org/doc/277416},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Guralnick, Robert
AU - Tiep, Pham
TI - A problem of Kollár and Larsen on finite linear groups and crepant resolutions
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 3
SP - 605
EP - 657
AB - The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age $\le 1$. More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation. As a consequence of our main results, we derive some properties of symmetric spaces $GU_d(\mathbb {C})/G$ having shortest closed geodesics of bounded length, and of quotients $\mathbb {C}^d/G$ having a crepant resolution.
LA - eng
KW - age; deviation; finite linear groups; complex reflection groups; crepant resolutions; quotient; finite linear group; complex reflection group; quotient
UR - http://eudml.org/doc/277416
ER -