Cette note donne une preuve élémentaire que les strates des différentiels abéliens ne contiennent pas de variétés algébriques complètes.
This note gives an elementary proof that the strata of abelian differentials do not contain complete algebraic varieties.
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@article{CRMATH_2020__358_2_197_0, author = {Gendron, Quentin}, title = {Les strates ne poss\`edent pas de vari\'et\'es compl\`etes}, journal = {Comptes Rendus. Math\'ematique}, pages = {197--200}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {2}, year = {2020}, doi = {10.5802/crmath.34}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/crmath.34/} }
TY - JOUR AU - Gendron, Quentin TI - Les strates ne possèdent pas de variétés complètes JO - Comptes Rendus. Mathématique PY - 2020 SP - 197 EP - 200 VL - 358 IS - 2 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.34/ DO - 10.5802/crmath.34 LA - fr ID - CRMATH_2020__358_2_197_0 ER -
Gendron, Quentin. Les strates ne possèdent pas de variétés complètes. Comptes Rendus. Mathématique, Tome 358 (2020) no. 2, pp. 197-200. doi : 10.5802/crmath.34. http://www.numdam.org/articles/10.5802/crmath.34/
[1] Geometry of algebraic curves. Volume II, Grundlehren der Mathematischen Wissenschaften, 268, Springer, 2011 | MR | Zbl
[2] Strata of -differentials, Algebr. Geom., Volume 6 (2019) no. 2, pp. 196-233 | MR | Zbl
[3] Affine geometry of strata of differentials, J. Inst. Math. Jussieu, Volume 18 (2019) no. 6, pp. 1331-1340 | DOI | MR | Zbl
[4] A bound on the dimensions of complete subvarieties of , Duke Math. J., Volume 51 (1984), pp. 405-408 | DOI | MR | Zbl
[5] On complete curves in moduli space. I. II., Math. Proc. Camb. Philos. Soc., Volume 110 (1991) no. 3, pp. 461-472 | DOI | MR | Zbl
[6] On the cohomology of strata of abelian differentials (2020) (https://arxiv.org/abs/2001.03227)
[7] Teichmüller curves, mainly from the viewpoint of algebraic geometry, Moduli spaces of Riemann surfaces (IAS/Park City Mathematics Series), Volume 20, American Mathematical Society ; Institute for Advanced Study, 2013, pp. 267-318 | DOI | Zbl
[8] Translation surfaces and their orbit closures : an introduction for a broad audience, EMS Surv. Math. Sci., Volume 2 (2015) no. 1, pp. 63-108 | DOI | MR | Zbl
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