Quasi-log canonical pairs are Du Bois
Authors:
Osamu Fujino and Haidong Liu
Journal:
J. Algebraic Geom. 31 (2022), 105-112
DOI:
https://doi.org/10.1090/jag/756
Published electronically:
February 1, 2021
Full-text PDF
Abstract |
References |
Additional Information
Abstract: We prove that every quasi-log canonical pair has only Du Bois singularities. Note that our arguments are free from the minimal model program.
References
- F. Ambro, Quasi-log varieties, Tr. Mat. Inst. Steklova 240 (2003), no. Biratsion. Geom. Lineĭn. Sist. Konechno Porozhdennye Algebry, 220–239; English transl., Proc. Steklov Inst. Math. 1(240) (2003), 214–233. MR 1993751
- Osamu Fujino, Fundamental theorems for the log minimal model program, Publ. Res. Inst. Math. Sci. 47 (2011), no. 3, 727–789. MR 2832805, DOI 10.2977/PRIMS/50
- Osamu Fujino, Fundamental theorems for semi log canonical pairs, Algebr. Geom. 1 (2014), no. 2, 194–228. MR 3238112, DOI 10.14231/AG-2014-011
- Osamu Fujino, Foundations of the minimal model program, MSJ Memoirs, vol. 35, Mathematical Society of Japan, Tokyo, 2017. MR 3643725
- O. Fujino, Fundamental properties of basic slc-trivial fibrations, Publ. Res. Inst. Math. Sci. (to appear).
- Osamu Fujino and Taro Fujisawa, Variations of mixed Hodge structure and semipositivity theorems, Publ. Res. Inst. Math. Sci. 50 (2014), no. 4, 589–661. MR 3273305, DOI 10.4171/PRIMS/145
- Osamu Fujino and Haidong Liu, On normalization of quasi-log canonical pairs, Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 10, 97–101. MR 3879320, DOI 10.3792/pjaa.94.97
- János Kollár, Singularities of the minimal model program, Cambridge Tracts in Mathematics, vol. 200, Cambridge University Press, Cambridge, 2013. With a collaboration of Sándor Kovács. MR 3057950, DOI 10.1017/CBO9781139547895
- János Kollár and Sándor J. Kovács, Log canonical singularities are Du Bois, J. Amer. Math. Soc. 23 (2010), no. 3, 791–813. MR 2629988, DOI 10.1090/S0894-0347-10-00663-6
- Sándor J. Kovács, Du Bois pairs and vanishing theorems, Kyoto J. Math. 51 (2011), no. 1, 47–69. MR 2784747, DOI 10.1215/0023608X-2010-020
- Sándor J. Kovács, The splitting principle and singularities, Compact moduli spaces and vector bundles, Contemp. Math., vol. 564, Amer. Math. Soc., Providence, RI, 2012, pp. 195–204. MR 2894635, DOI 10.1090/conm/564/11155
- J. H. M. Steenbrink, Vanishing theorems on singular spaces, Astérisque 130 (1985), 330–341. Differential systems and singularities (Luminy, 1983). MR 804061
References
- F. Ambro, Quasi-log varieties, Tr. Mat. Inst. Steklova 240 (2003), no. Biratsion. Geom. Lineĭn. Sist. Konechno Porozhdennye Algebry, 220–239; English transl., Proc. Steklov Inst. Math. 1(240) (2003), 214–233. MR 1993751
- Osamu Fujino, Fundamental theorems for the log minimal model program, Publ. Res. Inst. Math. Sci. 47 (2011), no. 3, 727–789. MR 2832805, DOI 10.2977/PRIMS/50
- Osamu Fujino, Fundamental theorems for semi log canonical pairs, Algebr. Geom. 1 (2014), no. 2, 194–228. MR 3238112, DOI 10.14231/AG-2014-011
- Osamu Fujino, Foundations of the minimal model program, MSJ Memoirs, vol. 35, Mathematical Society of Japan, Tokyo, 2017. MR 3643725
- O. Fujino, Fundamental properties of basic slc-trivial fibrations, Publ. Res. Inst. Math. Sci. (to appear).
- Osamu Fujino and Taro Fujisawa, Variations of mixed Hodge structure and semipositivity theorems, Publ. Res. Inst. Math. Sci. 50 (2014), no. 4, 589–661. MR 3273305, DOI 10.4171/PRIMS/145
- Osamu Fujino and Haidong Liu, On normalization of quasi-log canonical pairs, Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 10, 97–101. MR 3879320, DOI 10.3792/pjaa.94.97
- János Kollár, Singularities of the minimal model program, Cambridge Tracts in Mathematics, vol. 200, Cambridge University Press, Cambridge, 2013. MR 3057950, DOI 10.1017/CBO9781139547895
- János Kollár and Sándor J. Kovács, Log canonical singularities are Du Bois, J. Amer. Math. Soc. 23 (2010), no. 3, 791–813. MR 2629988, DOI 10.1090/S0894-0347-10-00663-6
- Sándor J. Kovács, Du Bois pairs and vanishing theorems, Kyoto J. Math. 51 (2011), no. 1, 47–69. MR 2784747, DOI 10.1215/0023608X-2010-020
- Sándor J. Kovács, The splitting principle and singularities, Compact moduli spaces and vector bundles, Contemp. Math., vol. 564, Amer. Math. Soc., Providence, RI, 2012, pp. 195–204. MR 2894635, DOI 10.1090/conm/564/11155
- J. H. M. Steenbrink, Vanishing theorems on singular spaces: Differential systems and singularities (Luminy, 1983), Astérisque 130 (1985), 330–341. MR 804061
Additional Information
Osamu Fujino
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
MR Author ID:
652921
Email:
fujino@math.sci.osaka-u.ac.jp
Haidong Liu
Affiliation:
Peking University, Beijing International Center for Mathematical Research, Beijing, 100871, People’s Republic of China
MR Author ID:
1243563
ORCID:
0000-0003-2385-9697
Email:
hdliu@bicmr.pku.edu.cn
Received by editor(s):
June 9, 2019
Received by editor(s) in revised form:
September 14, 2019
Published electronically:
February 1, 2021
Additional Notes:
The first author was partially supported by JSPS KAKENHI Grant Numbers JP16H03925, JP16H06337
Article copyright:
© Copyright 2021
University Press, Inc.
