TY - JOUR
T1 - Noether-Severi inequality and equality for irregular threefolds of general type
AU - Hu, Yong
AU - Zhang, Tong
N1 - Publisher Copyright:
© 2022 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2022/6/1
Y1 - 2022/6/1
N2 - We prove the optimal Noether-Severi inequality that vol(X)≥43χ(ωX) for all smooth and irregular 3-folds X of general type over C. For those 3-folds X attaining the equality, we completely describe their canonical models and show that the topological fundamental group π1(X)≃ℤ2. As a corollary, we obtain for the same X another optimal inequality that vol(X)≥43ha0(X,KX) where ha0(X,KX) stands for the continuous rank of KX, and we show that X attains this equality if and only if vol(X)=43χ(ωX).
AB - We prove the optimal Noether-Severi inequality that vol(X)≥43χ(ωX) for all smooth and irregular 3-folds X of general type over C. For those 3-folds X attaining the equality, we completely describe their canonical models and show that the topological fundamental group π1(X)≃ℤ2. As a corollary, we obtain for the same X another optimal inequality that vol(X)≥43ha0(X,KX) where ha0(X,KX) stands for the continuous rank of KX, and we show that X attains this equality if and only if vol(X)=43χ(ωX).
UR - https://www.scopus.com/pages/publications/85129295648
U2 - 10.1515/crelle-2022-0017
DO - 10.1515/crelle-2022-0017
M3 - 文章
AN - SCOPUS:85129295648
SN - 0075-4102
VL - 2022
SP - 241
EP - 273
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 787
ER -