Project ID: CNCS - UEFISCDI project number PN-III-P1-1.1-PD-2016-0182, contract no. 98 - 02/05/2018.

Project description: The project is devoted to solving some problems in the theory of functions of several complex variables, which are also related to complex analytic and algebraic geometry. These problems focus on pseudoconvexity of domains in the Euclidean complex space, the existence of Stein neighborhood basis for special subsets of the Euclidean complex space, projections of Stein domains, and properties of coverings of some special classes of complex spaces. The results obtained during this project will be published in relevant international journals.

Research team (in alphabetical order):

• Dr. Liviu Ornea (mentor)

• Dr. Ovidiu Preda (project coordinator)

Phase one of the project (02.05-2018 - 31.12.2018):

Achieved results in: pseudoconvexity, q-convexity, q-holomorphic convexity.

Article: G.-I. Ionita; O. Preda - q-pseudoconvex and q-holomorphically convex domains, arXiv:1809.00728 [math.CV], Math. Nachr. 292 (2019) pp.2619–2623.

Talks at conferences:

• On the projection of Stein domains - "The 22nd annual conference of SSMR", May 25-26, 2018, Corabia (Romania)

Participation in conferences (without presentation):

• CIME summer school “Complex non-Kähler geometry”, July 9-13, 2018, Cetraro (Italy);

• Workshop "Special metrics and symmetries on complex manifolds", September 11-14, 2018, Regensburg (Germany).

Phase two of the project (01.01-2019 - 31.12.2019):

Achieved results in: LCK metrics on singular spaces, coverings of LCK spaces.

Article: G.-I. Ionita; O. Preda - LCK metrics on complex spaces with quotient singularities, arXiv:1904.07119 [math.DG], Manuscripta Math. 162 (2020), pp.483-491.

Talks at conferences:

• Kaehler and locally conformally Kaehler metrics on complex spaces with singularities - 15th Romanian-Finnish Analysis Seminar, June 10–15, 2019, Turku (Finland);

• LCK metrics on complex spaces with quotient singularities - 9th Congress of Romanian Mathematicians, June 28 - July 3, 2019, Galati (Romania);

• Stein domains with prescribed projection in holomorphic fiber bundles - IMAR70, Conférence dédiée au 70ème anniversaire de l'Institut de Mathématiques de l'Académie Roumaine, October 4-5, 2019, Bucharest (Romania).

Phase three of the project (01.01-2020 - 30.04.2020):

Achieved results in: LCK complex spaces, ramified coverings of LCK complex spaces.

Article: O. Preda; M. Stanciu - Coverings of Locally Conformally Kaehler complex spaces, arXiv:1911.02379v2 [math.DG], Math. Z. 298 (2021) pp.639-651.