Timeline for Nef divisors on surfaces
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 14, 2021 at 21:07 | comment | added | Ennio Mori cone | One way would be to exhibit a single example of an degree 8 curve and 16 points with this property. I used a degree 8 curve obtained by a generic map $P^1\to P^2$ given by three degree 8 polynomials, computed the singular locus by hand, and saw that it was defined by forms of degree $\ge 7$. | |
| Sep 14, 2021 at 21:05 | comment | added | Ennio Mori cone | Note that if $C, C'$ are distinct irreducible curves, then $C\cdot C'\ge 0$ by the definition of the intersection product on surfaces. Since $2D$ is represented by an irreducible curve, the only curve it could potentially intersect negatively would be itself; but then $D^2=0$ shows that this doesn`t happen, so $D$ is nef. | |
| Sep 13, 2021 at 23:02 | comment | added | Puzzled | To show that $D$ is nef shouldn't one prove that $D\cdot C\geq 0$ for all curves $C\subset X$? Also, how do you check that if $C$ is general among the curves of degree $8$ with $16$ nodes then there is no quartic through the nodes? | |
| Sep 13, 2021 at 9:10 | review | Late answers | |||
| Sep 13, 2021 at 9:10 | |||||
| Sep 13, 2021 at 8:53 | history | answered | Ennio Mori cone | CC BY-SA 4.0 |