Real algebraic and pseudoholomorphic curves on the quadratic cone and smoothings of the singularity 𝑋₂₁

Orevkov, S.; Shustin, E.

doi:10.1090/spmj/1448

Real algebraic and pseudoholomorphic curves on the quadratic cone and smoothings of the singularity $X_{21}$
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by S. Yu. Orevkov and E. I. Shustin
Translated by: the authors

St. Petersburg Math. J. 28 (2017), 225-257

DOI: https://doi.org/10.1090/spmj/1448

Published electronically: February 15, 2017

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Abstract:

A fiberwise isotopy classification is completed for the smooth real algebraic and pseudoholomorphic curves of degree 8 on the quadratic cone that have a specially shaped oval crossing a given generating line of the cone at four real points. This classification is linked with an isotopy classification of smoothings of a real plane curve singularity that is the union of four smooth real local branches quadratically tangent to each other (the singularity $X_{21}$).

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