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.
Invariants of derived categories of sheaves; Rouquier isomorphism; fibrations; irregular varieties, non-vanishing loci.
Settore MAT/03 - Geometria
9-ott-2022
https://projecteuclid.org/journals/kyoto-journal-of-mathematics/advance-publication/Derived-equivalence-and-fibrations-over-curves-and-surfaces/10.1215/21562261-2022-0022.short
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/940389
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