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Seminar

Logarithmic vector fields and curve configurations December 10, 2012 (10:00AM PST - 11:00AM PST)
Location: MSRI: Simons Auditorium
Speaker(s) Hal Schenck
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Let A be the union U(C_i) of a finite number of smooth plane curves C_i, such that the singular points of A are quasihomogeneous. This means that locally (at a singular point), the equation of A is homogeneous. We prove that if C is a smooth curve such that the singularities of A U C are quasihomogeneous, then there is a short exact sequence relating the bundle of logarithmic derivations on A to the bundle of logarithmic derivations on A U C. This yields an inductive tool for studying the splitting of these bundles in terms of the geometry of the divisor A|_C on C.

(joint work with H. Terao and M. Yoshinaga, Hokkaido U.)

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