Given a smooth, projective curve Y , a finite group G and a positive integer n we study smooth, proper families X → Y × S → 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 HGn(Y ) is a fine moduli variety for this moduli problem and construct explicitly the universal family. For arbitrary G we prove that HGn (Y ) is a coarse moduli variety. For families of pointed Galois covers of (Y, y0) we prove that the Hurwitz space HGn (Y, y0) 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.
Vassil Kanev (2024). Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve. SERDICA MATHEMATICAL JOURNAL, 50(1), 47-102 [10.55630/serdica.2024.50.47-102].
Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve
Vassil Kanev
Primo
2024-04-05
Abstract
Given a smooth, projective curve Y , a finite group G and a positive integer n we study smooth, proper families X → Y × S → 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 HGn(Y ) is a fine moduli variety for this moduli problem and construct explicitly the universal family. For arbitrary G we prove that HGn (Y ) is a coarse moduli variety. For families of pointed Galois covers of (Y, y0) we prove that the Hurwitz space HGn (Y, y0) 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.File | Dimensione | Formato | |
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2024-047-102.pdf
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Descrizione: V. Kanev, Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve, Serdica Math. J. 50 (2024), 47–102.
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