Zeng CHEN , Guanxiang WANG . A VECTOR BUNDLE VALUED MIXED HARD LEFSCHETZ THEOREM[J]. Acta mathematica scientia, Series B, 2025 , 45(2) : 514 -524 . DOI: 10.1007/s10473-025-0213-8

[1] Berndtsson B, Sibony N. The $\overline{\partial}$-equation on a positive current. Invent Math, 2002, 147(2): 371-428
[2] Bauer W, Isralowitz J. Compactness characterization of operators in the Toeplitz algebra of the Fock space. J Funct Anal, 2012, 263: 1323-1355
[3] Cattani E. Mixed Lefschetz theorems and Hodge-Riemann bilinear relations. Int Math Res Not, 2008, 2008(9): Art rnn025
[4] Demailly J P.Analytic Methods in Algebraic Geometry. Surveys of Modern Mathematics. Somerville, MA: International Press, 2012
[5] Dinh T C, Nguyên V A. The mixed Hodge-Riemann bilinear relations for compact Kähler manifolds. Geom Funct Anal, 2006, 16(4): 838-849
[6] Dinh T C, Nguên V A. On the Lefschetz and Hodge-Riemann theorems. Illinois J Math, 2013, 57(1): 121-144
[7] Griffith P, Harris J.Principles of Algebraic Geometry. Reprint of the 1978 original. New York: John Wiley & Sons, 1994
[8] Gromov M.Convex sets and Kähler manifolds// Tricerri F. Advances in Differential Geometry and Topology. Singapore: World Sci Publishing, 1990: 1-38
[9] Garrido-Atienza M J, Marín-Rubio P. Navier Stokes equations with delays on unbounded domains. Nonlinear Anal, 2006, 64: 1100-1118
[10] Khovanskii A G. Newton polyhedra and the genus of complete intersections. Funkts Anal Prilozhen, 1978, 12(1): 51-61
[11] Khovanskii A G. The geometry of convex polyhedra and algebraic geometry. Uspehi Mat Nauk, 1979, 34(4): 160-161
[12] Khovanskii A G.Algebra and mixed volumes// Burago Y D, Zalgaller V A. Geometrical Inequalities. Series of Geometry 285. Berlin: Springer-Verlag, 1988: 182-207
[13] Kobayashi S.Differential Geometry of Complex Vector Bundles. Princeton: Princeton University Press, 1987
[14] Mcmullen P. On simple polytopes. Invent Math, 1993, 113(2): 419-444
[15] Mourougane C. Théorèmes d'annulation génériques pour les fibrés vectoriels semi-négatifs. Bull Soc Math Fr, 1999, 127: 115-133
[16] Málek J, Nečas J, Rokyta M, R$\dot{u}$žička M. Weak and Measure-valued Solutions to Evolutionary PDE. New York: Champman-Hall, 1996
[17] Simpson C T. Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization. J Amer Math Soc, 1988, 1(4): 867-918
[18] Simpson C T. Higgs bundles and local systems. Publications Mathématiques de l'IHÉS, 1992, 75: 5-95
[19] Takegoshi K. On cohomology groups of nef line bundles tensorized with multiplier ideal sheaves on compact Kähler manifolds. Osaka J Math, 1997, 34: 783-802
[20] Teissier B. Appendix: Sur une inégalité à la Minkowski pour les multiplicités, to ``An algebraic formula for the degree of a $\mathcal{C}^{\infty}$ map germ" (D.Eisenbud, H.Levine). Ann Math, 1979, 106(1): 19-44
[21] Teissier B. Du théorème de l'index de Hodge aux inégalités isopérimétriques. C R Acad Sci Paris Sér A-B, 1979, 288(4): 287-289
[22] Teissier B.Variétés toriques et polytopes// Bourbaki Seminar 1980/81. Springer Lecture Notes in Math 901. Berlin: Springer, 1981: 71-84
[23] Timorin V A. Mixed Hodge-Riemann bilinear relations in a linear context. Funct Anal Appl, 1998, 32(4): 268-272
[24] Wells R O.Differential Analysis on Complex Manifolds. New York: Springer-Verlag, 1980