On the unirationality of del Pezzo surfaces of degree 2

Cecília Salgado, Damiano Testa*, Anthony Várilly-Alvarado

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)

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 languageEnglish
Pages (from-to)121-139
Number of pages19
JournalJournal of the london mathematical society-Second series
Volume90
Issue number1
DOIs
Publication statusPublished - Aug-2014
Externally publishedYes

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