# Tagged Questions

**1**

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**2**answers

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### Embedded resolution of singularities

I'd like to check with my colleagues whether I have correctly understood "embedded resolution of singularities".
Let $X$ be a nonsingular projective variety over $\mathbf C$ and let $D$ be a "nice" ...

**14**

votes

**2**answers

887 views

### Bertini theorems for base-point-free linear systems in positive characteristics

Suppose that $X$ is a smooth algebraic variety over an algebraically closed (uncountable if it helps) field of characteristic $p > 0$. Suppose that $L$ is a line bundle, probably ample or at least ...

**5**

votes

**1**answer

467 views

### Stable base loci cannot contain isolated points

Let $X$ be a normal projective complex variety.
A theorem of Fujita-Zariski says that if $L$ is a Cartier divisor on $X$ such that
the base locus $Bs(|L|)$ is a finite set then $L$ is semiample.
It ...

**5**

votes

**2**answers

2k views

### The canonical line bundle of a normal variety

I have heard that the canonical divisor can be defined on a normal variety X since the smooth locus has codimension 2. Then, I have heard as well that for ANY algebraic variety such that the canonical ...

**2**

votes

**0**answers

229 views

### Proof of Saito criterion

Does it exist another proof of saito's criterion for free divisors, other than the one in "K. Saito, Theory of logarithmic differential forms and logarithmic vector fields, J. Fac. Sci. Univ. Tokyo ...

**2**

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**4**answers

708 views

### Examples of divisors on an analytical manifold

I am trying to understand divisors reading through Griffith and Harris but it is difficult to come up with any particular interesting example. I have browsed through Hartshone's book but everything is ...