Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve
Serdica Mathematical Journal, Tome 50 (2024) no. 1, pp. 47-102
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
Given a smooth, projective curve \(Y\), a finite group \(G\) and a positive integer $n$ we study smooth, proper families \(X\to Y\times S\to S\) of Galois covers of \(Y\) with Galois group isomorphic to $G$ branched in \(n\) points, parameterized by algebraic varieties \(S\). When \(G\) is with trivial center we prove that the Hurwitz space \(H^G_n(Y)\) is a fine moduli variety for this moduli problem and construct explicitly the universal family. For arbitrary \(G\) we prove that \(H^G_n(Y)\) is a coarse moduli variety. For families of pointed Galois covers of \((Y,y_0)\) we prove that the Hurwitz space \(H^G_n(Y,y_0)\) is a fine moduli variety, and construct explicitly the universal family, for arbitrary group \(G\). We use classical tools of algebraic topology and of complex algebraic geometry.
Keywords:
Galois cover of a curve, family of covers, Hurwitz space, moduli space, 14H30, 14H10, 14D22
@article{SMJ2_2024_50_1_a2,
author = {Kanev, Vassil},
title = {Hurwitz moduli varieties parameterizing {Galois} covers of an algebraic curve},
journal = {Serdica Mathematical Journal},
pages = {47--102},
publisher = {mathdoc},
volume = {50},
number = {1},
year = {2024},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_2024_50_1_a2/}
}
Kanev, Vassil. Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve. Serdica Mathematical Journal, Tome 50 (2024) no. 1, pp. 47-102. http://geodesic.mathdoc.fr/item/SMJ2_2024_50_1_a2/