All Questions

Maybe it sounds like a silly question but I'm not able to figure out in my head the geometric meaning of "twisting" vector bundles (or more generaly coherent sheaf) over $\mathbb{P}^n$. I ...

Let $X\subset\mathbb{P}^N$ be a quadratic manifold. That is $I(X)$ is generated by quadratic polynomials $Q_1,...,Q_m$. Let $\mathcal{I}_X$ be the ideal sheaf of $X$ and $\mathcal{I}_X/\mathcal{I}_X^...

Let $X\subset\mathbb{P}^n$ be an irreducible and reduced hypersurface of degree $d$. How can one explicitly compute the dimension of the vector spaces $H^0(X,T_X),H^1(X,T_X),H^2(X,T_X)$? Here $T_X$ is ...

Let $X\subset\mathbb{P}(a_0,...,a_N)$ be a smooth $n$-dimensional weighted complete intersection in a weighted projective space $\mathbb{P}(a_0,...,a_N)$. Is it true that if $q\geq 1$ then $H^0(X,\...