All Questions

Let $K$ be a field. A polynomial $F \in \mathbb{Q}[X_1, \dots, X_r]$ which is weighted homogeneous of degree $n$ with respect to the grading $\deg(X_k) = k$ is called numerically non-negative for nef ...

Let $X$ be a smooth (complex) projective $n$-dimensional variety ($n\geq 3$) and $\mathcal E$ a vector bundle of rank $r<n$ generated by its global sections on $X$. Let $\sigma\in H^0(\mathcal E)$ ...

I am trying to prove a conjecture that involves an enumerative problem. In the course of doing so, the following situation came up. I have a sequence of (smooth, complex, rationally connected) ...

Let $M$ be a smooth manifold of dimension $m$ and $\pi:E\rightarrow M$ a vector bundle of rank $e$. Given a section $s$ of the bundle $\pi:E\rightarrow M$, we expect that the zero locus $Z(s)$ of $s$ ...

This question is basically on applying the Grothendieck-Riemann-Roch theorem to finding a formula for the push-forward of a line bundle on $\mathbf{P}^r$ under a certain morphism. Since I have a lot ...