Serre duality


陳宗震 ( National Taiwan University )
2022-07-21  14:00 - 16:00
Room 201, Astronomy and Mathematics Building

Our first goal is the duality theorem on a projective scheme over an algebraically closed field. To prove that, we need the version of projective space and dualizing sheaf on projective space. We will see that Serre duality holds if and only if X is Cohen Macaulay and equidimensional.

Next, we will calculate the dualizing sheaf of local complete intersection in P_k^N, and show that the dualizing sheaf isomorphic to the canonical sheaf when X is a projective nonsingular variety over an algebraically closed field.

Finally, we will define the residues on a complete nonsingular curve, and prove the residue theorem.