Science China Mathematics

, Volume 62, Issue 11, pp 2331–2334 | Cite as

Logarithmic vanishing theorems for effective q-ample divisors

  • Kefeng LiuEmail author
  • Xueyuan Wan
  • Xiaokui Yang


Let X be a compact Kähler manifold and D be a simple normal crossing divisor. If D is the support of some effective q-ample divisor, we show
$$H^{i}(X, \Omega_{X}^{j}(\log D))=0, \quad \text { for } \quad i+j>n+q.$$


logarithmic vanishing theorems effective q-ample divisors simple normal crossing divisors compact Kahler manifolds 


32L20 53C55 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematical Sciences Research CenterChongqing University of Science and TechnologyChongqingChina
  2. 2.Department of MathematicsUniversity of California at Los AngelesLos AngelesUSA
  3. 3.School of MathematicsKorea Institute for Advanced StudySeoulRepublic of Korea
  4. 4.Department of Mathematics and Yau Mathematical Sciences CenterTsinghua UniversityBeijingChina

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