On projections of smooth and nodal plane curves
In this paper we prove the non-existence of Lagrangian embeddings of the Klein bottle K in R4 and CP2. We exploit the existence of a special embedding of K in a symplectic Lefschetz pencil pr:X→S2 and study its monodromy. As the main technical tool, we develop the combinatorial theory of mapping class groups. The results obtained enable us to show that in the case when the class [K]∈H2(X,Z2) is trivial, the monodromy of pr:X→S2 must be of a special form. Finally, we show that such a monodromy cannot be realized in CP2.
Получено обобщение результата Ильяшенко-Хованского, утверждающего, что разрешимость в квадратурах фуксовой системы с малыми коэффициентами эквивалентна ее треугольности. В работе этот результат обобщен на случай систем с малыми собственными значениями матриц вычетов.
В сборнике представлены полные тексты докладов (статьи) 2-й международной конференции по стохастическим методам и анализу данных (2nd Stochastic Modeling Techniques and Data Analysis International Conference, SMTDA-2012), которая проходила с 5 по 8 июня 2012 года в г. Ханья, Крит, Греция.
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