defn c1 CE29UWDY

defn c1

---

Definition 2.15. If E is a torsion-free coherent sheaf on X, one defines the determinant of E to be the rank-one reflexive sheaf det(E) = (Λrk(E)E)∨∨. Then, the first Chern class of E is c1(E) := c1(det E). (pdf) (Clarke 和 Tipler, 2023, p. 394)