Abstract
Among geometrically rational surfaces, del Pezzo surfaces of degree 2 over a field 푘 containing at least one point are arguably the simplest that are not known to be unirational over 푘. Looking for 푘‐rational curves on these surfaces, we extend some earlier work of Manin on this subject. We then focus on the case where 푘 is a finite field, where we show that all except possibly three explicit del Pezzo surfaces of degree 2 are unirational over 푘.
Original language | English |
---|---|
Pages (from-to) | 121-139 |
Number of pages | 19 |
Journal | Journal of the london mathematical society-Second series |
Volume | 90 |
Issue number | 1 |
DOIs | |
Publication status | Published - Aug-2014 |
Externally published | Yes |