Geodesic
Multiplicativity of the Double Ramification Cycle
Documenta mathematica, Tome 24 (2019), pp. 545-562.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The double ramification cycle satisfies a basic multiplicative relation $\mathrm{DRC}_a \cdot \mathrm{DRC}_b = \mathrm{DRC}_a \cdot \mathrm{DRC}_{a + b}$ 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 $\mathrm{b}$-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 $P_g^{d,k}(A)$ described by the second author in [\textit{F. Janda} et al., Publ. Math., Inst. Hautes Étud. Sci. 125, 221--266 (2017; Zbl 1370.14029)].
Classification : 14H10, 14C15, 30F30
Keywords: moduli space of curves, strata of differentials, double ramification cycles, tautological classes 
@article{DOCMA_2019__24__a47,
     author = {Holmes, David and Pixton, Aaron and Schmitt, Johannes},
     title = {Multiplicativity of the {Double} {Ramification} {Cycle}},
     journal = {Documenta mathematica},
     pages = {545--562},
     publisher = {mathdoc},
     volume = {24},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a47/}
}
TY  - JOUR
AU  - Holmes, David
AU  - Pixton, Aaron
AU  - Schmitt, Johannes
TI  - Multiplicativity of the Double Ramification Cycle
JO  - Documenta mathematica
PY  - 2019
SP  - 545
EP  - 562
VL  - 24
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a47/
LA  - en
ID  - DOCMA_2019__24__a47
ER  - 
%0 Journal Article
%A Holmes, David
%A Pixton, Aaron
%A Schmitt, Johannes
%T Multiplicativity of the Double Ramification Cycle
%J Documenta mathematica
%D 2019
%P 545-562
%V 24
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a47/
%G en
%F DOCMA_2019__24__a47
Holmes, David; Pixton, Aaron; Schmitt, Johannes. Multiplicativity of the Double Ramification Cycle. Documenta mathematica, Tome 24 (2019), pp. 545-562. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a47/