Determinant of an exact sequence sheafs
Hey everyone, I'm studying the Adjunction formula and part of the proof is confusing me. I have two exact sequences on a subvariety Y of codimension 1 in variety X:
where the are structure sheafs and (I think) are divisorial sheafs. We also have
Where these are tangent and normal bundles. The next line says "Taking determinants gives:"
which is the Adjunction formula. So can someone give me some insight into how one thinks about taking the determinants of something like an exact sequence?