Geodesic
A complete description of the cohomological invariants of even genus hyperelliptic curves
Documenta mathematica, Tome 26 (2021), pp. 199-230.

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

When the genus $g$ is even, we extend the computation of mod $2$ cohomological invariants of $\mathcal{H}_g$ to non algebraically closed fields, we give an explicit functorial description of the invariants and we completely describe their multiplicative structure. \par In the Appendix, we show that the cohomological invariants of the compactification $\overline{\mathcal{H}}_g$ are trivial, and use our methods to give a very short proof of a result by Cornalba on the Picard group of the compactification $\overline{\mathcal{H}}_g$ and extend it to positive characteristic.
Classification : 14H10, 14F43, 14D23, 14H30
Keywords: cohomological invariants, moduli of hyperelliptic curves, Chow groups with coefficients 
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     author = {Di Lorenzo, Andrea and Pirisi, Roberto},
     title = {A complete description of the cohomological invariants of even genus hyperelliptic curves},
     journal = {Documenta mathematica},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a51/}
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Di Lorenzo, Andrea; Pirisi, Roberto. A complete description of the cohomological invariants of even genus hyperelliptic curves. Documenta mathematica, Tome 26 (2021), pp. 199-230. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a51/