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Twistor lines in the period domain of complex tori. / Buskin, Nikolay; Izadi, Elham.

In: Geometriae Dedicata, Vol. 213, No. 1, 08.2021, p. 21-47.

Research output: Contribution to journal › Article › peer-review

Harvard

Buskin, N & Izadi, E 2021, 'Twistor lines in the period domain of complex tori', Geometriae Dedicata, vol. 213, no. 1, pp. 21-47. https://doi.org/10.1007/s10711-020-00566-y

APA

Buskin, N., & Izadi, E. (2021). Twistor lines in the period domain of complex tori. Geometriae Dedicata, 213(1), 21-47. https://doi.org/10.1007/s10711-020-00566-y

Vancouver

Buskin N, Izadi E. Twistor lines in the period domain of complex tori. Geometriae Dedicata. 2021 Aug;213(1):21-47. doi: 10.1007/s10711-020-00566-y

Author

Buskin, Nikolay ; Izadi, Elham. / Twistor lines in the period domain of complex tori. In: Geometriae Dedicata. 2021 ; Vol. 213, No. 1. pp. 21-47.

BibTeX

@article{11cdd052ad264832a24a8a49ec951b86,
title = "Twistor lines in the period domain of complex tori",
abstract = "As in the case of irreducible holomorphic symplectic manifolds, the period domain Compl of compact complex tori of even dimension 2n contains twistor lines. These are special 2-spheres parametrizing complex tori whose complex structures arise from a given quaternionic structure. In analogy with the case of irreducible holomorphic symplectic manifolds, we show that the periods of any two complex tori can be joined by a generic chain of twistor lines. We also prove a criterion of twistor path connectivity of loci in Compl where a fixed second cohomology class stays of Hodge type (1,1). Furthermore, we show that twistor lines are holomorphic submanifolds of Compl, of degree 2n in the Pl{\"u}cker embedding of Compl.",
keywords = "Complex tori, Hyperk{\"a}hler manifolds, Twistor lines, Twistor path connectivity, Twistor paths, Hyperkahler manifolds",
author = "Nikolay Buskin and Elham Izadi",
note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = aug,
doi = "10.1007/s10711-020-00566-y",
language = "English",
volume = "213",
pages = "21--47",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer Netherlands",
number = "1",

}

RIS

TY - JOUR

T1 - Twistor lines in the period domain of complex tori

AU - Buskin, Nikolay

AU - Izadi, Elham

N1 - Publisher Copyright: © 2020, Springer Nature B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/8

Y1 - 2021/8

N2 - As in the case of irreducible holomorphic symplectic manifolds, the period domain Compl of compact complex tori of even dimension 2n contains twistor lines. These are special 2-spheres parametrizing complex tori whose complex structures arise from a given quaternionic structure. In analogy with the case of irreducible holomorphic symplectic manifolds, we show that the periods of any two complex tori can be joined by a generic chain of twistor lines. We also prove a criterion of twistor path connectivity of loci in Compl where a fixed second cohomology class stays of Hodge type (1,1). Furthermore, we show that twistor lines are holomorphic submanifolds of Compl, of degree 2n in the Plücker embedding of Compl.

AB - As in the case of irreducible holomorphic symplectic manifolds, the period domain Compl of compact complex tori of even dimension 2n contains twistor lines. These are special 2-spheres parametrizing complex tori whose complex structures arise from a given quaternionic structure. In analogy with the case of irreducible holomorphic symplectic manifolds, we show that the periods of any two complex tori can be joined by a generic chain of twistor lines. We also prove a criterion of twistor path connectivity of loci in Compl where a fixed second cohomology class stays of Hodge type (1,1). Furthermore, we show that twistor lines are holomorphic submanifolds of Compl, of degree 2n in the Plücker embedding of Compl.

KW - Complex tori

KW - Hyperkähler manifolds

KW - Twistor lines

KW - Twistor path connectivity

KW - Twistor paths

KW - Hyperkahler manifolds

UR - http://www.scopus.com/inward/record.url?scp=85092495178&partnerID=8YFLogxK

U2 - 10.1007/s10711-020-00566-y

DO - 10.1007/s10711-020-00566-y

M3 - Article

AN - SCOPUS:85092495178

VL - 213

SP - 21

EP - 47

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1

ER -

ID: 26008171