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September 18, 2026
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On fields of meromorphic functions on neighborhoods of rational curves

Arnold Mathematical Journal. 2025. Vol. 11. No. 2. P. 133–153.
Serge Lvovski

Suppose that 𝐹 is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve with positive selfintersection. We prove that if there exists a non-constant meromorphic function on 𝐹, then the field of meromorphic functions on 𝐹 is isomorphic to the field of rational functions in one or two variables over ℂ.

Research target: Mathematics
Language: English
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Keywords: деформацииDeformationsalgebraic surfacesNeighborhoods of rational curvesокрестности рациональных кривыхалгебраические поверхности
Publication based on the results of:
Geometry of algebraic varieties, derived categories, motives, and metrics of special holonomy (2025)
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