# On explicit descent of marked curves and maps

@article{Sijsling2016OnED, title={On explicit descent of marked curves and maps}, author={Jeroen Sijsling and John Voight}, journal={Research in Number Theory}, year={2016}, volume={2}, pages={1-35} }

We revisit a statement of Birch that the field of moduli for a marked three-point ramified cover is a field of definition. Classical criteria due to Dèbes and Emsalem can be used to prove this statement in the presence of a smooth point, and in fact these results imply more generally that a marked curve descends to its field of moduli. We give a constructive version of their results, based on an algebraic version of the notion of branches of a morphism and allowing us to extend the… CONTINUE READING

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## Dessins, their delta-matroids and partial duals

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CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 50 REFERENCES

## On fields of moduli of curves

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## The Grothendieck theory of dessins d'enfants: Dessins from a geometric point of view

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Fields of moduli and fields of definition of curves

VIEW 1 EXCERPT

## On the algebraicity of generalized power series

VIEW 1 EXCERPT

## ON COMPUTING BELYI MAPS

VIEW 3 EXCERPTS

## The Grothendieck theory of dessins d'enfants

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL