On the positivity of direct image bundles
- 作者: Li Z.1, Zhou X.2,3
-
隶属关系:
- School of Science, Beijing University of Posts and Telecommunications
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences
- Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences
- 期: 卷 87, 编号 5 (2023)
- 页面: 140-163
- 栏目: Articles
- URL: https://ogarev-online.ru/1607-0046/article/view/140434
- DOI: https://doi.org/10.4213/im9336
- ID: 140434
如何引用文章
开放存取
##reader.subscriptionAccessGranted##
详细
In the present paper, we obtain an equivalent relation between the log-plurisubharmonicity of the relative Bergman kernel, the Griffiths and Nakano positivity for the direct image with the natural $L^2$ metric, by finding a converse of Berndtsson’s Theorem on the direct image. A converse of Berndtsson’s generalization of Kiselman minimal principle is also obtained.
全文:
作者简介
Zhi Li
School of Science, Beijing University of Posts and Telecommunications
Xiangyu Zhou
Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences
Email: xyzhou@math.ac.cn
PhD
参考
- B. Berndtsson, “Curvature of vector bundles associated to holomorphic fibrations”, Ann. of Math. (2), 169:2 (2009), 531–560
- B. Berndtsson, “Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains”, Ann. Inst. Fourier (Grenoble), 56:6 (2006), 1633–1662
- B. Berndtsson, M. Păun, “Bergman kernels and the pseudoeffectivity of relative canonical bundles”, Duke Math. J., 145:2 (2008), 341–378
- Fusheng Deng, Zhiwei Wang, Liyou Zhang, Xiangyu Zhou, New characterizations of plurisubharmonic functions and positivity of direct image sheaves
- Fusheng Deng, Jiafu Ning, Zhiwei Wang, Xiangyu Zhou, “Positivity of holomorphic vector bundles in terms of $L^p$-conditions for $overline{partial}$”, Math. Ann., 385:1-2 (2023), 575–607
- T. Inayama, “Nakano positivity of singular Hermitian metrics and vanishing theorems of Demailly–Nadel–Nakano type”, Algebr. Geom., 9:1 (2022), 69–92
- J.-P. Demailly, Complex analytic and differential geometry, 2012, 455 pp.
- Qi'an Guan, Xiangyu Zhou, “A solution of an $L^2$ extension problem with an optimal estimate and applications”, Ann. of Math. (2), 181:3 (2015), 1139–1208
- Qi'an Guan, XiangYu Zhou, “Strong openness of multiplier ideal sheaves and optimal $L^2$ extension”, Sci. China Math., 60:6 (2017), 967–976
- B. Berndtsson, L. Lempert, “A proof of the Ohsawa–Takegoshi theorem with sharp estimates”, J. Math. Soc. Japan, 68:4 (2016), 1461–1472
- A. Prekopa, “On logarithmic concave measures and functions”, Acta Sci. Math. (Szeged), 34 (1973), 335–343
- C. O. Kiselman, “The partial Legendre transformation for plurisubharmonic functions”, Invent. Math., 49:2 (1978), 137–148
- B. Berndtsson, “Prekopa's theorem and Kiselman's minimum principle for plurisubharmonic functions”, Math. Ann., 312:4 (1998), 785–792
- K. Ball, F. Barthe, A. Naor, “Entropy jumps in the presence of a spectral gap”, Duke Math. J., 119:1 (2003), 41–63
- D. Cordero-Erausquin, “On Berndtsson's generalization of Prekopa's theorem”, Math. Z., 249:2 (2005), 401–410
- L. Hörmander, “$L^2$ estimates and existence theorems for the $overline{partial}$ operator”, Acta. Math., 113:1 (1965), 89–152
- So-Chin Chen, Mei-Chi Shaw, Partial differential equations in several complex variables, AMS/IP Stud. Adv. Math., 19, Amer. Math. Soc., Providence, RI; International Press, Boston, MA, 2001, xii+380 pp.
- J.-P. Demailly, “Estimations $L^2$ pour l'operateur $overline{partial}$ d'un fibre vectoriel holomorphe semi-positif au-dessus d'une variete Kählerienne complète”, Ann. Sci. Ecole Norm. Sup. (4), 15:3 (1982), 457–511
- J.-P. Demailly, Analytic methods in algebraic geometry, Surv. Mod. Math., 1, International Press, Somerville, MA; Higher Education Press, Beijing, 2010/2012, viii+231 pp.
- T. Ohsawa, $L^2$ approaches in several complex variables. Development of Oka–Cartan theory by $L^2$ estimates for the $overlinepartial$ operator, Springer Monogr. Math., Springer, Tokyo, 2015, ix+196 pp.
- Xiangyu Zhou, “A survey on $L^2$ extension problem”, Complex geometry and dynamics, Abel Symp., 10, Springer, Cham, 2015, 291–309
- T. Ohsawa, K. Takegoshi, “On the extension of $L^2$ holomorphic functions”, Math. Z., 195:2 (1987), 197–204
- W. Rudin, Real and complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1987, xiv+416 pp.
- V. Guedj, A. Zeriahi, Degenerate complex Monge–Ampère equations, EMS Tracts Math., 26, Eur. Math. Soc. (EMS), Zürich, 2017, xxiv+472 pp.
- L. Hörmander, Notions of convexity, Progr. Math., 127, Birkhäuser Boston, Inc., Boston, MA, 1994, viii+414 pp.
- L. Lempert, “Modules of square integrable holomorphic germs”, Analysis meets geometry, Trends Math., Birkhäuser/Springer, Cham, 2017, 311–333
- Zhuo Liu, Hui Yang, Xiangyu Zhou, “New properties of multiplier submodule sheaves”, C. R. Math. Acad. Sci. Paris, 360 (2022), 1205–1212
- Zhuo Liu, Hui Yang, Xiangyu Zhou, On the multiplier submodule sheaves associated to singular Nakano semi-positive metrics
- H. Raufi, Log concavity for matrix-valued functions and a matrix-valued Prekopa theorem
- F. Maitani, H. Yamaguchi, “Variation of Bergman metrics on Riemann surfaces”, Math. Ann., 330:3 (2004), 477–489
补充文件
