Iacono, Donatella Deformations and obstructions of pairs (\(X, D\)). (English) Zbl 1349.14041 Int. Math. Res. Not. 2015, No. 19, 9660-9695 (2015). Summary: We study infinitesimal deformations of pairs \((X,D)\) with \(X\) smooth projective variety and \(D\) a smooth or a normal crossing divisor, defined over an algebraically closed field of characteristic \(0\). Using the differential-graded Lie algebras theory and the Cartan homotopy construction, we are able to prove in a completely algebraic way the unobstructedness of the deformations of the pair \((X,D)\) in many cases, for example, whenever \((X,D)\) is a log Calabi-Yau pair, in the case of a smooth divisor \(D\) in a Calabi-Yau variety \(X\) and when \(D\) is a smooth divisor in \(|-m K_X|\), for some positive integer \(m\). Cited in 12 Documents MSC: 14D15 Formal methods and deformations in algebraic geometry 14C20 Divisors, linear systems, invertible sheaves PDFBibTeX XMLCite \textit{D. Iacono}, Int. Math. Res. Not. 2015, No. 19, 9660--9695 (2015; Zbl 1349.14041) Full Text: DOI arXiv