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

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 3, page 605-657
- ISSN: 1435-9855

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topGuralnick, 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 -

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