Tautological rings of spaces of pointed genus two curves of compact type
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Tautological rings of spaces of pointed genus two curves of compact type. / Petersen, Dan Erik.
I: Compositio Mathematica, Bind 152, Nr. 7, 01.07.2016, s. 1398-1420.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Tautological rings of spaces of pointed genus two curves of compact type
AU - Petersen, Dan Erik
PY - 2016/7/1
Y1 - 2016/7/1
N2 - We prove that the tautological ring of , the moduli space of -pointed genus two curves of compact type, does not have Poincaré duality for any. This result is obtained via a more general study of the cohomology groups of. We explain how the cohomology can be decomposed into pieces corresponding to different local systems and how the tautological cohomology can be identified within this decomposition. Our results allow the computation of for any and considered both as -representation and as mixed Hodge structure/ -adic Galois representation considered up to semi-simplification. A consequence of our results is also that all even cohomology of is tautological for
AB - We prove that the tautological ring of , the moduli space of -pointed genus two curves of compact type, does not have Poincaré duality for any. This result is obtained via a more general study of the cohomology groups of. We explain how the cohomology can be decomposed into pieces corresponding to different local systems and how the tautological cohomology can be identified within this decomposition. Our results allow the computation of for any and considered both as -representation and as mixed Hodge structure/ -adic Galois representation considered up to semi-simplification. A consequence of our results is also that all even cohomology of is tautological for
KW - cohomology of moduli spaces
KW - Faber conjectures
KW - Gromov-Witten theory
KW - moduli of curves
KW - tautological ring
UR - http://www.scopus.com/inward/record.url?scp=84975108511&partnerID=8YFLogxK
U2 - 10.1112/S0010437X16007478
DO - 10.1112/S0010437X16007478
M3 - Journal article
AN - SCOPUS:84975108511
VL - 152
SP - 1398
EP - 1420
JO - Compositio Mathematica
JF - Compositio Mathematica
SN - 0010-437X
IS - 7
ER -
ID: 165569622