The derived Bézout theorem
時 間：2023-11-08 14:00 (星期三) / 地 點：S101 / 茶 會：S205 (13:30)
Given two smooth algebraic curves of degrees and in the complex projective plane, Bezout’s theorem is a classical result asserting that the intersection consists of either infinitely many or exactly points, counted with multiplicities. Generalizing this formula to intersections in higher-dimensional projective space was a task that fuelled much of 20th century algebraic geometry, eventually culminating in J.-P. Serre’s solution in 1958.
We will review some of this history before presenting a 21st century point of view on Bézout’s theorem. Specifically, we will see that the modern language of derived algebraic geometry allows us to give a simple definition of intersection multiplicities, which unlike Serre’s formula applies even to non-proper intersections, and yields a vast generalization of Bézout theorem for arbitrary intersections of projective hypersurfaces.