Essential dimension of moduli of curves and other algebraic stacks

Brosnan, Patrick, Reichstein, Zinovy, and Vistoli, Angelo. "Essential dimension of moduli of curves and other algebraic stacks." Journal of the European Mathematical Society 013.4 (2011): 1079-1112. <http://eudml.org/doc/277591>.

@article{Brosnan2011,
abstract = {In this paper we consider questions of the following type. Let $k$ be a base field and $K/k$ be a field extension. Given a geometric object $X$ over a field $K$ (e.g. a smooth curve of genus $g$), what is the least transcendence degree of a field of definition of $X$ over the base field $k$? In other words, how many independent parameters are needed to define $X$? To study these questions we introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete answer to the question above when the geometric objects $X$ are smooth, stable or hyperelliptic curves. The appendix, written by Najmuddin Fakhruddin, answers this question in the case of abelian varieties.},
author = {Brosnan, Patrick, Reichstein, Zinovy, Vistoli, Angelo},
journal = {Journal of the European Mathematical Society},
keywords = {essential dimension; stack; gerbe; moduli of curves; moduli of abelian varieties; essential dimension; stack; gerbe; moduli of curves; moduli of abelian varieties},
language = {eng},
number = {4},
pages = {1079-1112},
publisher = {European Mathematical Society Publishing House},
title = {Essential dimension of moduli of curves and other algebraic stacks},
url = {http://eudml.org/doc/277591},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Brosnan, Patrick
AU - Reichstein, Zinovy
AU - Vistoli, Angelo
TI - Essential dimension of moduli of curves and other algebraic stacks
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 4
SP - 1079
EP - 1112
AB - In this paper we consider questions of the following type. Let $k$ be a base field and $K/k$ be a field extension. Given a geometric object $X$ over a field $K$ (e.g. a smooth curve of genus $g$), what is the least transcendence degree of a field of definition of $X$ over the base field $k$? In other words, how many independent parameters are needed to define $X$? To study these questions we introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete answer to the question above when the geometric objects $X$ are smooth, stable or hyperelliptic curves. The appendix, written by Najmuddin Fakhruddin, answers this question in the case of abelian varieties.
LA - eng
KW - essential dimension; stack; gerbe; moduli of curves; moduli of abelian varieties; essential dimension; stack; gerbe; moduli of curves; moduli of abelian varieties
UR - http://eudml.org/doc/277591
ER -