Kodaira dimension and zeros of holomorphic one-forms. (English) Zbl 1297.14011

In this very interesting article, the authors use generic vanishing theorems for Hodge modules on abelian varieties to prove that if \(X\) is a smooth complex projective variety of general type and \(0\neq \omega \in H^0(\Omega ^1_X)\) is a global holomorphic 1-form, then the zero locus of \(\omega\) is non-empty.


14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14K05 Algebraic theory of abelian varieties
32C38 Sheaves of differential operators and their modules, \(D\)-modules
32C05 Real-analytic manifolds, real-analytic spaces
Full Text: DOI arXiv


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