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Mat. Sb., 2018, Volume 209, Number 8, Pages 56–65 (Mi msb9032)  

This article is cited in 1 scientific paper (total in 1 paper)

On divisors of small canonical degree on Godeaux surfaces

Vik. S. Kulikov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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, Godeaux surfaces.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.


DOI: https://doi.org/10.4213/sm9032

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English version:
Sbornik: Mathematics, 2018, 209:8, 1155–1163

Bibliographic databases:

Document Type: Article
UDC: 512.7
MSC: Primary 13N15, 14J25; Secondary 37K10
Received: 31.10.2017 and 02.12.2017

Citation: Vik. S. Kulikov, “On divisors of small canonical degree on Godeaux surfaces”, Mat. Sb., 209:8 (2018), 56–65; Sb. Math., 209:8 (2018), 1155–1163

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. B. Zheglov, “Surprising examples of nonrational smooth spectral surfaces”, Sb. Math., 209:8 (2018), 1131–1154  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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