Search Results

I have been having trouble understanding some statements regarding flatness in Hartshorne - in particular relating to some of the examples in the text. Any help would be appreciated! Here is the iss …

Take two intersecting lines $L_1,L_2$ in $\mathbb{P}^3$. Blow-up $L_1$, and then blow up the strict transform $L_2'$ of $L_2$ and call $E_2$ the exceptional divisor of this second blow-up. $E_2$ is a …

Let $C$ be a smooth curve of degree $d$ in $\mathbb{P}^2$ over $\mathbb{C}$. Say $C$ is defined by $p(x,y,z)=0$, with $p$ a homogeneous degree $d$ polynomial. In vector calculus one learns that the g …

Is there any geometric way to understand the exact sequence in Example 8.20.1 in Ch II of Hartshorne (p. 182), or its dual from theorem 8.13? Here is the sequence: $0\to O_{\mathbb{P}^n}\to O_{\math …

Is there a good way to find the fan and polytope of the blow-up of $\mathbb{P}^3$ along the union of two invariant intersecting lines? Everything I find in the literature is for blow-ups along smooth …