Volume 22, issue 2 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 27
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Pixton's double ramification cycle relations

Emily Clader and Felix Janda

Geometry & Topology 22 (2018) 1069–1108
Bibliography
1 R Cavalieri, Hurwitz theory and the double ramification cycle, Jpn. J. Math. 11 (2016) 305 MR3544920
2 R Cavalieri, S Marcus, J Wise, Polynomial families of tautological classes on g,nrt, J. Pure Appl. Algebra 216 (2012) 950 MR2864866
3 A Chiodo, Stable twisted curves and their r–spin structures, Ann. Inst. Fourier (Grenoble) 58 (2008) 1635 MR2445829
4 A Chiodo, Towards an enumerative geometry of the moduli space of twisted curves and rth roots, Compos. Math. 144 (2008) 1461 MR2474317
5 A Chiodo, Y Ruan, LG/CY correspondence : the state space isomorphism, Adv. Math. 227 (2011) 2157 MR2807086
6 A Chiodo, D Zvonkine, Twisted r–spin potential and Givental’s quantization, Adv. Theor. Math. Phys. 13 (2009) 1335 MR2672465
7 E Clader, Relations on g,n via orbifold stable maps, Proc. Amer. Math. Soc. 145 (2017) 11 MR3565356
8 T Coates, A Givental, H H Tseng, Virasoro constraints for toric bundles, preprint (2015) arXiv:1508.06282
9 C Deninger, J Murre, Motivic decomposition of abelian schemes and the Fourier transform, J. Reine Angew. Math. 422 (1991) 201 MR1133323
10 J Ebert, O Randal-Williams, Stable cohomology of the universal Picard varieties and the extended mapping class group, Doc. Math. 17 (2012) 417 MR2946828
11 C Faber, R Pandharipande, Relative maps and tautological classes, J. Eur. Math. Soc. 7 (2005) 13 MR2120989
12 A B Givental, Gromov–Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1 (2001) 551 MR1901075
13 A B Givental, Semisimple Frobenius structures at higher genus, Int. Math. Res. Not. 2001 (2001) 1265 MR1866444
14 T Graber, R Pandharipande, Constructions of nontautological classes on moduli spaces of curves, Michigan Math. J. 51 (2003) 93 MR1960923
15 S Grushevsky, K Hulek, Geometry of theta divisors: a survey, from: "A celebration of algebraic geometry" (editors B Hassett, J McKernan, J Starr, R Vakil), Clay Math. Proc. 18, Amer. Math. Soc. (2013) 361 MR3114948
16 S Grushevsky, D Zakharov, The double ramification cycle and the theta divisor, Proc. Amer. Math. Soc. 142 (2014) 4053 MR3266977
17 R Hain, Normal functions and the geometry of moduli spaces of curves, from: "Handbook of moduli, I" (editors G Farkas, I Morrison), Adv. Lect. Math. 24, International (2013) 527 MR3184171
18 F Janda, Comparing tautological relations from the equivariant Gromov–Witten theory of projective spaces and spin structures, preprint (2014) arXiv:1407.4778
19 F Janda, Relations in the tautological ring and Frobenius manifolds near the discriminant, preprint (2015) arXiv:1505.03419
20 F Janda, R Pandharipande, A Pixton, D Zvonkine, Double ramification cycles on the moduli spaces of curves, Publ. Math. Inst. Hautes Études Sci. 125 (2017) 221 MR3668650
21 P Johnson, Equivariant GW theory of stacky curves, Comm. Math. Phys. 327 (2014) 333 MR3183403
22 M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
23 S Marcus, J Wise, Stable maps to rational curves and the relative Jacobian, preprint (2013) arXiv:1310.5981
24 A Marian, D Oprea, R Pandharipande, A Pixton, D Zvonkine, The Chern character of the Verlinde bundle over g,n, J. Reine Angew. Math. 732 (2017) 147
25 T E Milanov, H H Tseng, Equivariant orbifold structures on the projective line and integrable hierarchies, Adv. Math. 226 (2011) 641 MR2735771
26 S Morita, Families of Jacobian manifolds and characteristic classes of surface bundles, I, Ann. Inst. Fourier (Grenoble) 39 (1989) 777 MR1030850
27 S Morita, Families of Jacobian manifolds and characteristic classes of surface bundles, II, Math. Proc. Cambridge Philos. Soc. 105 (1989) 79 MR966142
28 R Pandharipande, A Pixton, D Zvonkine, Relations on g,n via 3–spin structures, J. Amer. Math. Soc. 28 (2015) 279 MR3264769
29 A Pixton, Conjectural relations in the tautological ring of Mg,n, preprint (2012) arXiv:1207.1918
30 A Pixton, The tautological ring of the moduli space of curves, PhD thesis, Princeton University (2013) MR3153424
31 A. Pixton, Double ramification cycles and tautological relations on Mg,n, preprint (2014)
32 O Randal-Williams, Relations among tautological classes revisited, Adv. Math. 231 (2012) 1773 MR2964623
33 S Shadrin, L Spitz, D Zvonkine, Equivalence of ELSV and Bouchard–Mariño conjectures for r–spin Hurwitz numbers, Math. Ann. 361 (2015) 611 MR3319543
34 C Teleman, The structure of 2D semi-simple field theories, Invent. Math. 188 (2012) 525 MR2917177
35 H H Tseng, Orbifold quantum Riemann–Roch, Lefschetz and Serre, Geom. Topol. 14 (2010) 1 MR2578300
36 C Voisin, Chow rings and decomposition theorems for families of K3 surfaces and Calabi–Yau hypersurfaces, Geom. Topol. 16 (2012) 433 MR2916291