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Beijing–Moscow Mathematics Colloquium
21 января 2022 г. 11:00–12:00, г. Москва, online
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Real algebraic and real pseudoholomorphic curves
S. Yu. Orevkovab a Université Paul Sabatier, Toulouse
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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Аннотация:
According to Gromov's theory, smooth symplectic 2-surfaces in CP^2 share many properties with complex algebraic curves. The same phenomenon takes place in the real case. Namely, smooth symplectic surfaces invariant under the complex conjugation (we call them real
pseudoholomorphic curves) have many common properties with plane projective real algebraic curves.
An open question (Symplectic Isotopy Problem): does each connected component of the space of symplectic surfaces contain an algebraic curve? The same question can be asked in the real case and an negative answer will be given in the talk. We shall prove certain inequalities for the complex orientations of plane real algebraic curves which are
not satisfied by an infinite series of real pseudoholomorphic curves.
Язык доклада: английский
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