Geodesic
The closure of double ramification loci via strata of exact differentials
Documenta mathematica, Tome 27 (2022), pp. 2625-2656 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

Double ramification loci, also known as strata of 0-differentials, are algebraic subvarieties of the moduli space of smooth curves parametrizing Riemann surfaces such that there exists a rational function with prescribed ramification over 0 and ∞. We describe the closure of double ramification loci inside the Deligne–Mumford compactification in geometric terms. To a rational function we associate its exact differential, which allows us to realize double ramification loci as linear subvarieties of strata of meromorphic differentials. We then obtain a geometric description of the closure using our recent results on the boundary of linear subvarieties. Our approach yields a new way of relating the geometry of loci of rational functions and Teichmüller dynamics. We also compare our results to a different approach using admissible covers.
DOI : 10.4171/dm/x37
Classification : 14H15
Mots-clés : moduli space of curves, double ramification cycles, strata of differentials 
@article{10_4171_dm_x37,
     author = {Frederik Benirschke},
     title = {The closure of double ramification loci via strata of exact differentials},
     journal = {Documenta mathematica},
     pages = {2625--2656},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x37},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x37/}
}
TY  - JOUR
AU  - Frederik Benirschke
TI  - The closure of double ramification loci via strata of exact differentials
JO  - Documenta mathematica
PY  - 2022
SP  - 2625
EP  - 2656
VL  - 27
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/x37/
DO  - 10.4171/dm/x37
ID  - 10_4171_dm_x37
ER  - 
%0 Journal Article
%A Frederik Benirschke
%T The closure of double ramification loci via strata of exact differentials
%J Documenta mathematica
%D 2022
%P 2625-2656
%V 27
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/x37/
%R 10.4171/dm/x37
%F 10_4171_dm_x37
Frederik Benirschke. The closure of double ramification loci via strata of exact differentials. Documenta mathematica, Tome 27 (2022), pp. 2625-2656. doi: 10.4171/dm/x37

Cité par Sources :