TY - JOUR
T1 - Albanese fibrations of surfaces with low slope
AU - Ling, Songbo
AU - Lü, Xin
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2025/3
Y1 - 2025/3
N2 - Let S be a minimal irregular surface of general type, whose Albanese map induces a fibration f:S→C of genus g. We prove a linear upper bound on the genus g if KS2≤4χ(OS), namely (Formula presented.) Examples are constructed showing that the above linear upper bound is sharp. We also give a characterization of the Albanese fibrations reaching the above upper bound when χ(OS)≥5. On the other hand, we will construct a sequence of surfaces Sn of general type with KSn2/χ(OSn)>4 and with an Albanese fibration fn, such that the genus gn of a general fiber of fn increases quadratically with χ(OSn), and that KSn2/χ(OSn) can be arbitrarily close to 4.
AB - Let S be a minimal irregular surface of general type, whose Albanese map induces a fibration f:S→C of genus g. We prove a linear upper bound on the genus g if KS2≤4χ(OS), namely (Formula presented.) Examples are constructed showing that the above linear upper bound is sharp. We also give a characterization of the Albanese fibrations reaching the above upper bound when χ(OS)≥5. On the other hand, we will construct a sequence of surfaces Sn of general type with KSn2/χ(OSn)>4 and with an Albanese fibration fn, such that the genus gn of a general fiber of fn increases quadratically with χ(OSn), and that KSn2/χ(OSn) can be arbitrarily close to 4.
UR - https://www.scopus.com/pages/publications/85209204457
U2 - 10.1007/s00208-024-03037-x
DO - 10.1007/s00208-024-03037-x
M3 - 文章
AN - SCOPUS:85209204457
SN - 0025-5831
VL - 391
SP - 4641
EP - 4671
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3
ER -