Logarithmic vector fields for quasihomogeneous curve configurations in P^2

Hal Schenck; Hiroaki Terao; Masahiko Yoshinaga

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arXiv · 1407.3237

Logarithmic vector fields for quasihomogeneous curve configurations in P^2

Hal Schenck·Hiroaki Terao·Masahiko Yoshinaga

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Abstract

Let A be a union of smooth plane curves C_i, such that each singular point of A is quasihomogeneous. We prove that if C is a smooth curve such that each singular point of A U C is also quasihomogeneous, then there is an elementary modification of rank two bundles, which relates the O_{P^2} module Der(log A) of vector fields on P^2 tangent to A to the module Der(log A U C). This yields an inductive tool for studying the splitting of the bundles Der(log A) and Der(log A U C), depending on the geometry of the divisor A|_C on C.

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Hal Schenck, Hiroaki Terao, Masahiko Yoshinaga. 2014-07-11. Logarithmic vector fields for quasihomogeneous curve configurations in P^2. https://arxiv.org/abs/1407.3237

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