Using stacks to impose tangency conditions on curves

Cadman, Charles

doi:10.1353/ajm.2007.0007

Cited by 186 publications

(208 citation statements)

References 14 publications

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“…In the following lemma, we use a slightly more general notion of a root of Cartier divisors that is a root of invertible sheaves with global sections. All the properties of Section 1.3.b are still true (see [Cad07] or [ℵGV08]). …”

Section: Toric Deligne-mumford Stacks Versus Stacky Fansmentioning

confidence: 97%

Smooth toric Deligne-Mumford stacks

Fantechi

Mann

Nironi

2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

132

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Abstract. We give a geometric definition of smooth toric Deligne-Mumford stacks using the action of a"torus". We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.

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Section: Toric Deligne-mumford Stacks Versus Stacky Fansmentioning

confidence: 97%

Smooth toric Deligne-Mumford stacks

Fantechi

Mann

Nironi

2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

132

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“…Cadman décrit dans [16] les faisceaux inversibles sur une courbe tordue lisse sur une base connexe et noethérienne (corollaire 3. …”

Section: Courbes Tordues D'abramovich Et Vistoliunclassified

Foncteur de Picard d’un champ algébrique

Brochard

2008

Math. Ann.

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RésuméIn this article we study the Picard functor and the Picard stack of an algebraic stack. We give a new and direct proof of the representability of the Picard stack. We prove that it is quasi-separated, and that the connected component of the identity is proper when the fibers of X are geometrically normal. We study some examples of Picard functors of classical stacks. In an appendix, we review the lisse-étale cohomology of abelian sheaves on an algebraic stack.

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“…If X is a scheme, D is an effective Cartier divisor, and r is a natural number, then [7] and [3] introduced the stack X D,r , called the root of a line bundle with a section. The following result is essential for our application: By combining these two results, we obtain a simple description of the cohomology of the twisted sectors of I(M g ) whose general element is a cyclic cover of a genus 0 curve: Corollary 4.6.…”

Section: The Compactification Of the Inertia Stack Of M Gmentioning

confidence: 99%

The orbifold cohomology of moduli of genus 3 curves

Pagani

Tommasi

2013

manuscripta math.

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Abstract. In this work we study the additive orbifold cohomology of the moduli stack of smooth genus g curves. We show that this problem reduces to investigating the rational cohomology of moduli spaces of cyclic covers of curves where the genus of the covering curve is g. Then we work out the case of genus g = 3. Furthermore, we determine the part of the orbifold cohomology of the Deligne-Mumford compactification of the moduli space of genus 3 curves that comes from the Zariski closure of the inertia stack of M3.

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Using stacks to impose tangency conditions on curves

Cited by 186 publications

References 14 publications

Smooth toric Deligne-Mumford stacks

Smooth toric Deligne-Mumford stacks

Foncteur de Picard d’un champ algébrique

The orbifold cohomology of moduli of genus 3 curves

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