Timeline for Existence of pencils on some special curves of genus 10
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 11, 2016 at 23:57 | comment | added | roy smith | technically we need also to rule out a hyperelliptic curve, since then there would be g(1,3)'s with base point. But among the curve of g(1,4)'s there is one whose general divisor does not contain a divisor of the g(1,2) so we get again that the genus is ≤ 3. | |
| Jan 9, 2016 at 18:00 | comment | added | roy smith | at least for base point free pencils, how's this? If C admits maps of degrees both 3 and 4 to P^1, then the product map to P^1xP^1 is generically injective, so the genus of C is ≤ 6. The same argument (of Castelnuovo) shows a curve with base point free pencils of relatively prime degrees d,e has genus ≤ (d-1)(e-1). | |
| Dec 19, 2015 at 11:26 | vote | accept | Heitor | ||
| Dec 18, 2015 at 13:08 | answer | added | Jason Starr | timeline score: 5 | |
| Dec 18, 2015 at 12:15 | history | asked | Heitor | CC BY-SA 3.0 |