TY - JOUR
T1 - Quartic del Pezzo surfaces over function fields of curves
AU - Hassett, Brendan
AU - Tschinkel, Yuri
N1 - Funding Information:
The first author was supported by National Science Foundation Grants 0901645, 0968349, and 1148609; the second author was supported by National Science Foundation Grants 0739380, 0968318, and 1160859. We are grateful to Asher Auel, Jean-Louis Colliot-Thélène, and Raman Parimala for useful conversations as well as to Andrew Kresch and Nikita Kozin for comments on the manuscript; we appreciate Jason Starr and Yi Zhu explaining the results of [35] on Abel–Jacobi morphisms for fibrations of rationally connected varieties over curves.
PY - 2014
Y1 - 2014
N2 - We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of sections to the fibration, and mappings to the intermediate Jacobian of the total space. We exhibit examples where these are birational, which has applications to arithmetic questions, especially over finite fields.
AB - We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of sections to the fibration, and mappings to the intermediate Jacobian of the total space. We exhibit examples where these are birational, which has applications to arithmetic questions, especially over finite fields.
KW - Del Pezzo surfaces
KW - Fibrations
KW - Function fields of curves
KW - Intermediate Jacobians
KW - Rational points
UR - http://www.scopus.com/inward/record.url?scp=84890883568&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84890883568&partnerID=8YFLogxK
U2 - 10.2478/s11533-013-0354-1
DO - 10.2478/s11533-013-0354-1
M3 - Article
AN - SCOPUS:84890883568
SN - 1895-1074
VL - 12
SP - 395
EP - 420
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
IS - 3
ER -