TY - JOUR
T1 - On the slope conjecture of Barja and Stoppino for fibred surfaces
AU - Lu, Xin
AU - Zuo, Kang
N1 - Publisher Copyright:
© 2019 Scuola Normale Superiore. All rights reserved.
PY - 2019
Y1 - 2019
N2 - Let f : X ! B be a locally non-trivial relatively minimal fibration of genus g ≥ 2 with relative irregularity q f . It was conjectured by Barja and Stoppino that the slope λ f ≥ 4 g ( - g - q 1 f ). On the one hand, we show the lower bound λ f > g 4 - (g q - f 1 / ) 2 , and also prove the Barja-Stoppino conjecture when q f is small with respect to g. On the other hand, we construct counterexamples violating the conjectured bound when g is odd and q f = (g + 1)/2.
AB - Let f : X ! B be a locally non-trivial relatively minimal fibration of genus g ≥ 2 with relative irregularity q f . It was conjectured by Barja and Stoppino that the slope λ f ≥ 4 g ( - g - q 1 f ). On the one hand, we show the lower bound λ f > g 4 - (g q - f 1 / ) 2 , and also prove the Barja-Stoppino conjecture when q f is small with respect to g. On the other hand, we construct counterexamples violating the conjectured bound when g is odd and q f = (g + 1)/2.
UR - https://www.scopus.com/pages/publications/85058050706
U2 - 10.2422/2036-2145.201611_008
DO - 10.2422/2036-2145.201611_008
M3 - 文章
AN - SCOPUS:85058050706
SN - 0391-173X
VL - 19
SP - 1025
EP - 1064
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
JF - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
IS - 3
ER -