EMMA LEPRI

PhD Graduate

PhD program:: XXXV


supervisor: D. Fiorenza
advisor: M. Manetti

Thesis title: L-infinity morphisms and semiregularity

The main topic of this thesis is the construction of canonical $L_{\infty}$ liftings of the components of the Buchweitz-Flenner semiregularity map for coherent sheaves on complex manifolds, using Chern-Simons classes for curved DG-pairs. As an application, we obtain that the Buchweitz-Flenner semiregularity map annihilates all obstructions to deformations of a coherent sheaf on a complex projective manifold. We also introduce semiregularity maps for a Lie pair $(\mathcal{L}, \mathcal{A})$ and a locally free $\mathcal{A}$-module, and prove they annihilate all obstructions to deformations of the $\mathcal{A}$-module, provided that a certain spectral sequence degenerates at $E_1$.

Research products

11573/1699507 - 2023 - L∞ liftings of semiregularity maps via Chern–Simons classes
Bandiera, R.; Lepri, E.; Manetti, M. - 01a Articolo in rivista
paper: ADVANCES IN MATHEMATICS (-SAN DIEGO, USA: ACADEMIC PRESS INC ELSEVIER SCIENCES -Brugge, Belgium [etc.] Academic Press, 1965-) pp. - - issn: 0001-8708 - wos: WOS:001122377300001 (1) - scopus: 2-s2.0-85174355678 (1)

11573/1555699 - 2021 - Connections and L∞ liftings of semiregularity maps
Lepri, E.; Manetti, M. - 01a Articolo in rivista
paper: JOURNAL OF GEOMETRY AND PHYSICS (Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598) pp. - - issn: 0393-0440 - wos: WOS:000687953900013 (3) - scopus: 2-s2.0-85107664382 (3)

11573/1375558 - 2020 - On deformations of diagrams of commutative algebras
Lepri, E.; Manetti, M. - 02a Capitolo o Articolo
book: Springer INdAM Series - (978-3-030-37113-5; 978-3-030-37114-2)

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