scholarly journals The κ ring of the moduli of curves of compact type

2012 ◽  
Vol 208 (2) ◽  
pp. 335-388 ◽  
Author(s):  
Rahul Pandharipande
Keyword(s):  
Moduli Of Curves ◽  
Compact Type

Constancy of Jacobi osculating rank of g.o. spaces of compact and non-compact type

2011 ◽  
Vol 105 (1) ◽  
pp. 207-221 ◽  
Author(s):  
T. Arias-Marco ◽  
A. Arvanitoyeorgos ◽  
A. M. Naveira
Keyword(s):  
Compact Type

scholarly journals Birational geometry of moduli of curves with an S3-cover

2021 ◽  
Vol 389 ◽  
pp. 107898
Author(s):  
Mattia Galeotti
Keyword(s):  
Moduli Of Curves ◽  
Birational Geometry

Study on fracture transferability from compact type specimen to pipe for 316LN stainless steel

2021 ◽  
pp. 104437
Author(s):  
R. Nikhil ◽  
S.A. Krishnan ◽  
G. Sasikala ◽  
A. Moitra ◽  
Shaju K. Albert ◽  
...  
Keyword(s):  
Stainless Steel ◽  
Type Specimen ◽  
Compact Type ◽  
316Ln Stainless Steel

scholarly journals Tautological rings of spaces of pointed genus two curves of compact type

2016 ◽  
Vol 152 (7) ◽  
pp. 1398-1420 ◽  
Author(s):  
Dan Petersen
Keyword(s):  
Hodge Structure ◽  
Galois Representation ◽  
Mixed Hodge Structure ◽  
Poincaré Duality ◽  
General Study ◽  
Compact Type ◽  
Poincare Duality ◽  
Tautological Ring ◽  
Genus Two ◽  
Tautological Rings

We prove that the tautological ring of ${\mathcal{M}}_{2,n}^{\mathsf{ct}}$, the moduli space of $n$-pointed genus two curves of compact type, does not have Poincaré duality for any $n\geqslant 8$. This result is obtained via a more general study of the cohomology groups of ${\mathcal{M}}_{2,n}^{\mathsf{ct}}$. 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 $H^{k}({\mathcal{M}}_{2,n}^{\mathsf{ct}})$ for any $k$ and $n$ considered both as $\mathbb{S}_{n}$-representation and as mixed Hodge structure/$\ell$-adic Galois representation considered up to semi-simplification. A consequence of our results is also that all even cohomology of $\overline{{\mathcal{M}}}_{2,n}$ is tautological for $n<20$, and that the tautological ring of $\overline{{\mathcal{M}}}_{2,n}$ fails to have Poincaré duality for all $n\geqslant 20$. This improves and simplifies results of the author and Orsola Tommasi.

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