Seshadri constants on P¹¹, and a solution to the symplectic packing problem

In this paper we compute the r-point Seshadri constant on P¹¹ for those line bundles where the answer might be expected to be governed by $(-1)$-curves. As a consequence we solve the symplectic packing problem for P¹¹. Some results on the r-point Seshadri constant for other line bundles are given. These latter results use a useful new "reflection method". In the analysis there is a striking difference between the cases when r is odd and when r is even. When r is even the problem admits an infinite order automorphism, and there are infinitely many $(-1)$-curves to consider. In contrast, when r is odd only a finite number (usually $4$) types of $(-1)$-curves are relevant to our answer.