Symplectic configurations: a homological and computer-aided approach
We formulated a homological and computer-aided approach to study certain unions of symplectic surfaces, called symplectic configurations, in a rational $4$-manifold $X=CP^2\# N\overline{CP^2}$. We addressed several fundamental theoretical questions, and also as a technical device, developed a symplectic analog of the so-called quadratic Cremona transformations in complex algebraic geometry. As an application, we gave a new proof that a certain line arrangement in $CP^2$, called Fano planes, doe…
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