Weprovethattheboundedderivedcategoryofcoherentsheavesonasmoothprojective complex variety reconstructs the isomorphism classes of fibrations onto smooth projective curves of genus g ≥ 2. Moreover, in dimension at most four, we prove that the same category reconstructs the isomorphism classes of fibrations onto normal projective surfaces with positive holomorphic Euler characteristic and admitting a finite morphism to an abelian variety. Finally, we study the derived invariance of a class of fibrations with minimal base-dimension under the condition that all the Hodge numbers of type h^{0,p}(X) are derived invariant.
Derived equivalence and fibrations over curves and surfaces / L. Lombardi. - In: KYOTO JOURNAL OF MATHEMATICS. - ISSN 2156-2261. - (2022), pp. 1-18. [Epub ahead of print] [10.1215/21562261-2022-0022]
Derived equivalence and fibrations over curves and surfaces
L. Lombardi
2022
Abstract
Weprovethattheboundedderivedcategoryofcoherentsheavesonasmoothprojective complex variety reconstructs the isomorphism classes of fibrations onto smooth projective curves of genus g ≥ 2. Moreover, in dimension at most four, we prove that the same category reconstructs the isomorphism classes of fibrations onto normal projective surfaces with positive holomorphic Euler characteristic and admitting a finite morphism to an abelian variety. Finally, we study the derived invariance of a class of fibrations with minimal base-dimension under the condition that all the Hodge numbers of type h^{0,p}(X) are derived invariant.File | Dimensione | Formato | |
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