2007
DOI: 10.1007/s00209-007-0173-9
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Picard group of moduli of hyperelliptic curves

Abstract: Abstract. The main subject of this work is the difference between the coarse moduli space and the stack of hyperelliptic curves. We compute their Picard groups, giving explicit description of the generators. We get an application to the non-existence of a tautological family over the coarse moduli space.

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Cited by 16 publications
(20 citation statements)
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“…Moreover (Proposition 7.4), we express the tautological λ classes of Mumford ([Mum83]) in terms of the explicit generators. In the hyperelliptic case we recover the result of [GV08].…”
Section: Introductionsupporting
confidence: 77%
“…Moreover (Proposition 7.4), we express the tautological λ classes of Mumford ([Mum83]) in terms of the explicit generators. In the hyperelliptic case we recover the result of [GV08].…”
Section: Introductionsupporting
confidence: 77%
“…As observed in [10] the Chern classes of V g are not tautological classes. Gorchinskiy and Viviani show that the first Hodge class λ equals (g/2)c 1 .…”
Section: Proof Of Theorem 11mentioning
confidence: 84%
“…Following [2] and [10] we know that given a family of hyperelliptic curves π : X → S the map π factors as π = p • f where p : P → S is a Brauer-Severi variety and f : X → P is a double cover. Then f * O X = O P ⊕ L where L is a line-bundle such that L 2 = O P (−D) where D ⊂ P is the ramification divisor.…”
Section: Proof Of Theorem 11mentioning
confidence: 99%
“…In these remaining cases, we have constructed a morphism S → S that is bijective on points but not an isomorphism. It is possible that no family C → S inducing such an isomorphism exists; see [12] for results in this direction for hyperelliptic curves.…”
Section: Construction Of Representative Familiesmentioning
confidence: 99%