Twistor lines in the period domain of complex tori
| Autor: | Nikolay Buskin, E. Izadi |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics math.CV Twistor path connectivity General Mathematics Holomorphic function Complex tori Algebraic geometry 14C30 01 natural sciences Domain (mathematical analysis) Twistor theory Mathematics - Algebraic Geometry math.AG Chain (algebraic topology) Primary 14K20 0103 physical sciences FOS: Mathematics Complex Variables (math.CV) 0101 mathematics Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics Mathematics - Complex Variables Twistor lines 010102 general mathematics Secondary 53C26 Pure Mathematics Cohomology Hyperkahler manifolds math.DG Differential Geometry (math.DG) 32J27 Differential geometry Twistor paths Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology Primary 14K20 Secondary 53C26 14C30 32J27 Symplectic geometry |
| Zdroj: | Buskin, N; & Izadi, E. (2018). Twistor lines in the period domain of complex tori. UC San Diego: Retrieved from: http://www.escholarship.org/uc/item/9nv2g8jp GEOMETRIAE DEDICATA, vol 213, iss 1 Geometriae Dedicata, vol 213, iss 1 |
| ISSN: | 1572-9168 0046-5755 |
| DOI: | 10.1007/s10711-020-00566-y |
| Popis: | 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 {\em 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\"ucker embedding of $Compl$. Comment: 29 pages, 2 figures. Theorem 2 and Corollary 3 have been added in the new version |
| Databáze: | OpenAIRE |
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