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Creators/Authors contains: "Taji, Behrouz"

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  1. ; (, Cambridge University Press)
    Hacon, Christopher; Xu, Chenyang (Ed.)
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  2. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract We develop a Hodge theoretic invariant for families of projective manifolds that measures the potential failure of an Arakelov-type inequality in higher dimensions, one that naturally generalizes the classical Arakelov inequality over regular quasi-projective curves.We show that, for families of manifolds with ample canonical bundle, this invariant is uniformly bounded.As a consequence, we establish that such families over a base of arbitrary dimension satisfy the aforementioned Arakelov inequality, answering a question of Viehweg. 
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  3. ; (, Mathematische Zeitschrift)
    Abstract We show that, for any fixed weight, there is a natural system of Hodge sheaves, whose Higgs field has no poles, arising from a flat projective family of varieties parametrized by a regular complex base scheme, extending the analogous classical result for smooth projective families due to Griffiths. As an application, based on positivity of direct image sheaves, we establish a criterion for base spaces of rational Gorenstein families to be of general type. A key component of our arguments is centered around the construction of derived categorical objects generalizing relative logarithmic forms for smooth maps and their functorial properties. 
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