Geodesic
On divisors of small canonical degree on Godeaux surfaces
Sbornik. Mathematics, Tome 209 (2018) no. 8, pp. 1155-1163

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Pre-spectral data $(X,C,D)$ coding the rank-1 commutative subalgebras of a certain completion $\widehat D$ of the algebra of differential operators $D=k[[x_1,x_2]][\partial_1,\partial_2]$, where $k$ is an algebraically closed field of characteristic 0, are shown to exist. Here $X$ is a Godeaux surface, $C$ is an effective ample divisor represented by a smooth curve, $h^0(X,\mathscr O_X(C))=1$ and $D$ is a divisor on $X$ satisfying the conditions $(D, C)_X=g(C)-1$, $h^i(X,\mathscr O_X(D))=0$ for $i=0,1,2$ and $h^0(X,\mathscr O_X(D+C))=1$. Bibliography: 26 titles.
Keywords: pre-spectral data for commutative subalgebras of rank $1$, algebras of differential operators
Mots-clés : Godeaux surfaces. 
@article{SM_2018_209_8_a2,
     author = {Vik. S. Kulikov},
     title = {On divisors of small canonical degree on {Godeaux} surfaces},
     journal = {Sbornik. Mathematics},
     pages = {1155--1163},
     publisher = {mathdoc},
     volume = {209},
     number = {8},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_8_a2/}
}
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Vik. S. Kulikov. On divisors of small canonical degree on Godeaux surfaces. Sbornik. Mathematics, Tome 209 (2018) no. 8, pp. 1155-1163. http://geodesic.mathdoc.fr/item/SM_2018_209_8_a2/