Loading...
Please wait, while we are loading the content...
Similar Documents
Blow-ups of surfaces
| Content Provider | Semantic Scholar |
|---|---|
| Author | Koughnett, Paul Van |
| Copyright Year | 2014 |
| Abstract | where PicX is the Picard group. Thus, we identify PicX with the group of divisors mod the divisors of rational functions; two divisors are said to be linearly equivalent if they differ by the divisor of a rational function. More explicitly, the divisor D is associated to the line bundle O(D) of rational functions with ‘poles along D.’ I introduced a couple of relations weaker than linear equivalence. Two divisors are algebraically equivalent if they are the fibers of a relative Cartier divisor over a connected base scheme, D ⊆X ×S → S. Recall that the group PicX is the k-points of the group scheme PicX ; geometrically, then, we see that two divisors are algebraically equivalent if they’re on the same connected component of the Picard scheme. The Néron-Severi group is defined to be the group of divisors mod algebraic equivalence, |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.uchicago.edu/~dwilson/k3notes/Lecture5-Blowups.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
