Geodesic
Multiplicativity of the Double Ramification Cycle
Documenta mathematica, Tome 24 (2019), pp. 545-562
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

The double ramification cycle satisfies a basic multiplicative relation DRCa​⋅DRCb​=DRCa​⋅DRCa+b​ over the locus of compact-type curves, but this relation fails in the Chow ring of the moduli space of stable curves. We restore this relation over the moduli space of stable curves by introducing an extension of the double ramification cycle to the small b-Chow ring (the colimit of the Chow rings of all smooth blowups of the moduli space). We use this to give evidence for the conjectured equality between the (twisted) double ramification cycle and a cycle Pgd,k​(A) described by the second author in [F. Janda et al., Publ. Math., Inst. Hautes Étud. Sci. 125, 221–266 (2017; Zbl 1370.14029)].
DOI : 10.4171/dm/688
Classification : 14C15, 14H10, 30F30
Mots-clés : moduli space of curves, tautological classes, double ramification cycles, strata of differentials 
@article{10_4171_dm_688,
     author = {David Holmes and Johannes Schmitt and Aaron Pixton},
     title = {Multiplicativity of the {Double} {Ramification} {Cycle}},
     journal = {Documenta mathematica},
     pages = {545--562},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/688},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/688/}
}
TY  - JOUR
AU  - David Holmes
AU  - Johannes Schmitt
AU  - Aaron Pixton
TI  - Multiplicativity of the Double Ramification Cycle
JO  - Documenta mathematica
PY  - 2019
SP  - 545
EP  - 562
VL  - 24
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/688/
DO  - 10.4171/dm/688
ID  - 10_4171_dm_688
ER  - 
%0 Journal Article
%A David Holmes
%A Johannes Schmitt
%A Aaron Pixton
%T Multiplicativity of the Double Ramification Cycle
%J Documenta mathematica
%D 2019
%P 545-562
%V 24
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/688/
%R 10.4171/dm/688
%F 10_4171_dm_688
David Holmes; Johannes Schmitt; Aaron Pixton. Multiplicativity of the Double Ramification Cycle. Documenta mathematica, Tome 24 (2019), pp. 545-562. doi: 10.4171/dm/688

Cité par Sources :