Consider a triangle $ABC$ in the projective plane $\mathbb{P}^2.$ For a point $p \in \mathbb{P}^2$ one can define its trilinear polar line $t(p)$ (see here). This defines a birational map to the dual plane $$t\colon \mathbb{P}^2 \longrightarrow (\mathbb{P}^2)^{\vee}.$$ As an abstract map to a projective plane it is defined by the linear system $|2H-A-B-C|,$ but I don't see, how one can naturally understand the duality from this perspective.
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asked Sep 7, 2019 at 17:03
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$\begingroup$ what is $H$ here? $\endgroup$– Dima PasechnikCommented Sep 7, 2019 at 17:56
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$\begingroup$ The divisor class of a line. $\endgroup$– Daniil RudenkoCommented Sep 7, 2019 at 18:13
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