Geodesic
$k$-differentials on curves and rigid cycles in moduli space
Documenta mathematica, Tome 26 (2021), pp. 1817-1850 Cet article a éte moissonné depuis la source EMS Press

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For g≥2,j=1,...,g and n≥g+j we exhibit infinitely many new rigid and extremal effective codimension j cycles in Mg,n​, the Deligne-Mumford compactification of the moduli of n-pointed curves of genus g. The extremal cycles constructed correspond to the strata of quadratic differentials and projections of these strata under forgetful morphisms. We further show the same holds for k-differentials with k≥3 if the strata are irreducible. We compute the class of the divisors in the case of quadratic differentials which contain the first known examples of effective divisors on Mg,n​ with negative ψi​ coefficients.
DOI : 10.4171/dm/857
Classification : 14C20, 14C25, 14E30
Mots-clés : divisors, moduli of curves, rigid cycles, Teichmüller dynamics 
@article{10_4171_dm_857,
     author = {Scott Mullane},
     title = {$k$-differentials on curves and rigid cycles in moduli space},
     journal = {Documenta mathematica},
     pages = {1817--1850},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/857},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/857/}
}
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Scott Mullane. $k$-differentials on curves and rigid cycles in moduli space. Documenta mathematica, Tome 26 (2021), pp. 1817-1850. doi: 10.4171/dm/857

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