1
vote
2answers
257 views

Producing $(-2)$ curves on a smooth surface

We know that blowing up a point on a surface produces a $(-1)$ curve. Is there any such standard techniques to produce $(-2)$ curves in a smooth surface?
2
votes
1answer
279 views

Log resolutions on surfaces and 3-folds in characteristic p

If $X$ is a normal projective variety and $D$ a divisor in it, we say that $\pi\colon (\widetilde X,\widetilde D)\rightarrow (X,D)$ is a log resolution if $\widetilde X$ is a resolution of $X$, the ...
2
votes
2answers
371 views

The exceptional locus of a minimal resolution of singularities

Let X be a surface. (A surface is an excellent integral normal separated 2-dimensional scheme.) Let $\psi:Y\longrightarrow X$ be a minimal resolution of singularities and let $E$ be an irreducible ...