Author:
Popovici Dan,Stelzig Jonas,Ugarte Luis
Abstract
AbstractWe extend the notion of small essential deformations of Calabi–Yau complex structures from the case of the Iwasawa manifold, for which they were introduced recently by the first-named author, to the general case of page-1-$$\partial {{\bar{\partial }}}$$
∂
∂
¯
-manifolds that were jointly introduced very recently by all three authors. We go on to obtain an analogue of the unobstructedness theorem of Bogomolov, Tian and Todorov for Calabi–Yau page-1-$$\partial {{\bar{\partial }}}$$
∂
∂
¯
-manifolds. As applications of this discussion, we study the small deformations of certain Nakamura solvmanifolds and reinterpret the cases of the Iwasawa manifold and its 5-dimensional analogue from this standpoint.
Funder
Ludwig-Maximilians-Universität München
Publisher
Springer Science and Business Media LLC
Reference20 articles.
1. Angella, D., Kasuya, H.: Bott-Chern cohomology of solvmanifolds. Ann. Glob. Anal. Geom. 52(4), 363–411 (2017)
2. Hasegawa, K.: Small Deformations and non-left-invariant complex structures on six-dimensional compact solvmanifolds. Differ. Geom. Appl. 28(2), 220–227 (2010)
3. Kawamata, Y.: Unobstructed deformations—a remark on a paper of Z. Ran. J. Algebraic Geom. 1, 183–190 (1992) (Erratum in J. Alg.Geom 6 (1997), 803–804)
4. Kodaira, K., Spencer, D.C.: On deformations of complex analytic structures, III. Stability theorems for complex structures. Ann. Math. 71(1), 43–76 (1960)
5. Kuranishi, M.: On the locally complete families of complex analytic structures. Ann. Math. 75(3), 536–577 (1962)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献