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1
V Arena , S
Canning , E Clader , R Haburcak , A Q
Li , S C Mok , C Tamborini , Holomorphic forms
and non-tautological cycles on moduli spaces of curves ,
Selecta Math. 31 (2025) 47 MR4901039
2
S Canning , H
Larson , On the Chow and cohomology rings of moduli
spaces of stable curves , preprint (2022) arXiv:2208.02357
3
S Canning , H
Larson , S Payne , The eleventh cohomology
group of ℳ g,n , Forum Math. Sigma 11 (2023)
MR4616435
4
S Canning , H
Larson , S Payne , Extensions of tautological rings
and motivic structures in the cohomology of ℳ g,n , preprint (2023) arXiv:2307.08830
5
S Canning , H
Larson , J Schmitt , The
Gorenstein property and Pixton’s conjecture for compact type
moduli , in preparation (2024)
6
S Canning , D
Oprea , R Pandharipande , Cycles on the
moduli space of principally polarized abelian
varieties , Invent. Math. (2025)
7
E Clader , F
Janda , Pixton’s double
ramification cycle relations , Geom. Topol. 22 (2018)
1069 MR3748684
8
V Delecroix , J
Schmitt , J van Zelm , admcycles – a Sage
package for calculations in the tautological ring of the moduli
space of stable curves , J. Softw. Algebra Geom. 11
(2021) 89 MR4387186
9
C Faber , A
conjectural description of the tautological ring of the moduli
space of curves , from: "Moduli of curves and abelian
varieties" (editors C Faber, E Looijenga), Aspects Math. E33,
Friedr. Vieweg (1999) 109 MR1722541
10
C Faber , R
Pandharipande , Logarithmic series and
Hodge integrals in the tautological ring , Michigan
Math. J. 48 (2000) 215 MR1786488
11
C Faber , R
Pandharipande , Relative maps and
tautological classes , J. Eur. Math. Soc. 7 (2005) 13
MR2120989
12
T Graber , R
Pandharipande , Constructions of
nontautological classes on moduli spaces of curves ,
Michigan Math. J. 51 (2003) 93 MR1960923
13
T Graber , R
Vakil , On the
tautological ring of ℳ g,n , Turkish J. Math. 25 (2001)
237 MR1829089
14
R Hain , E
Looijenga , Mapping class
groups and moduli spaces of curves , from: "Algebraic
geometry—Santa Cruz 1995" (editors J Kollár, R Lazarsfeld,
D R Morrison), Proc. Sympos. Pure Math. 62.2, Amer. Math.
Soc. (1997) 97 MR1492535
15
F Janda , Relations on
M g,n via equivariant Gromov–Witten theory
of ℙ 1 , Algebr. Geom. 4 (2017) 311
MR3652083
16
F Janda , Frobenius manifolds
near the discriminant and relations in the tautological
ring , Lett. Math. Phys. 108 (2018) 1649 MR3802725
17
S Keel , Intersection theory of moduli
space of stable n -pointed curves
of genus zero , Trans. Amer. Math. Soc. 330 (1992) 545
MR1034665
18
C Lian , The ℋ -tautological ring , Selecta Math. 27
(2021) 96 MR4320845
19
C Lian , Non-tautological
Hurwitz cycles , Math. Z. 301 (2022) 173 MR4405647
20
R Pandharipande ,
Three questions in Gromov–Witten theory , from:
"Proceedings of the International Congress of Mathematicians,
II" (editor T Li), Higher Ed. (2002) 503 MR1957060
21
R Pandharipande ,
A
calculus for the moduli space of curves , from:
"Algebraic geometry : Salt Lake City 2015" (editors T de
Fernex, B Hassett, M Mustaţă, M Olsson, M Popa, R Thomas),
Proc. Sympos. Pure Math. 97.1, Amer. Math. Soc. (2018) 459
MR3821159
22
R Pandharipande , A
Pixton , D Zvonkine , Relations on
ℳ g,n via 3 -spin structures , J. Amer. Math. Soc.
28 (2015) 279 MR3264769
23
D Petersen ,
The
structure of the tautological ring in genus one , Duke
Math. J. 163 (2014) 777 MR3178432
24
D Petersen ,
Tautological
rings of spaces of pointed genus two curves of compact
type , Compos. Math. 152 (2016) 1398 MR3530445
25
D Petersen , O
Tommasi , The Gorenstein
conjecture fails for the tautological ring of ℳ 2 ,n ,
Invent. Math. 196 (2014) 139 MR3179574
26
A Pixton , The tautological
ring of the moduli space of curves , PhD thesis,
Princeton University (2013) MR3153424
27
J Schmitt , J van
Zelm , Intersections of
loci of admissible covers with tautological classes ,
Selecta Math. 26 (2020) 79 MR4177576
28
J van Zelm ,
Nontautological
bielliptic cycles , Pacific J. Math. 294 (2018) 495
MR3770123