All Questions

Let $X$ be a smooth, quasi-projective variety of dimension $n$ and $\mathcal{F}$ be a globally generated coherent sheaf supported on a codimension two subvariety $V \subset X$. Is $c_2(\mathcal{F}) \...

Let $D=D_1\cup D_2$ be a simple normal crossing (snc) divisor in a smooth complex projective variety $X$. Let $E=\mathcal{O}_X(V_1)\oplus \mathcal{O}_X(V_2)$. Then, obviousely, $$ c(E)\equiv 1+c_1(E)+...

Let $X$ be a smooth projective variety and $Z$ a closed subvariety of co-dimension $k$. The first $k-1$ chern classes of the ideal sheaf of $Z$ vanishes and the $k$-th chern class is given by ...

Let $X$ be a smooth projective variety over an algebraically closed field $k$ and $\mathcal E$ a family on torsion free coherent sheaves on $X$ parametrized by a smooth curve (over $k$) i.e. a ...