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Mathematics > Algebraic Geometry

arXiv:2201.03088 (math)
[Submitted on 9 Jan 2022 (v1), last revised 27 Mar 2022 (this version, v2)]

Title:Viro-Zvonilov inequalities for flexible curves on an almost complex four-dimensional manifold

Authors:V. I. Zvonilov
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Abstract:The restrictions on the topology of nonsingular plane projective real algebraic curves of odd degree, obtained by O. Viro and the author in the paper published in the early 90s, are extended to flexible curves lying on an almost complex four-dimensional manifold. Some examples of real algebraic surfaces and real curves on them prove the sharpness of the obtained inequalities.
In addition, it is proved that a compact Lie group smooth action can be lifted to a cyclic branched covering space $ \tilde{X} $ over a closed four-dimensional manifold, and a sufficient condition for $ H_1(\tilde{X})=0 $ was found.
Comments: 13 pages, 2 figures, to be published in: Lobachevskii Journal Of Mathematics, Vol.43, No.3, (1922), pp.1473--1480
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14P25, 32Q60, 57M12, 57S25, 14H45
Cite as: arXiv:2201.03088 [math.AG]
  (or arXiv:2201.03088v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2201.03088

Submission history

From: Victor Zvonilov [view email]
[v1] Sun, 9 Jan 2022 20:47:29 UTC (31 KB)
[v2] Sun, 27 Mar 2022 17:16:42 UTC (31 KB)
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