These $2$-spheres are called 'twistor lines'. They indeed cover the moduli space (in the non-polarized case) : more precisely, any two points of the moduli space may be linked by a chain of twistor lines.

A reference where this is nicely explained (and used !) is Huybrecht's Bourbaki talk about Verbitsky's Torelli theorem : http://arxiv.org/abs/1106.5573. See particularly paragraphs 3.2 and 4.4.

In the polarized case, no twistor line is included in the moduli space, as a general member is not projective : see remark 8.1 of http://arxiv.org/abs/1009.0413. This article is particularly interesting in this respect. Indeed, Charles and Markman prove the standard conjectures for some projective hyperkähler varieties (a statement peculiar to projective varieties) using deformations along a twistor line (hence using non-projective varieties).

These $2$-spheres are called 'twistor lines'. They indeed cover the moduli space (in the non-polarized case) : more precisely, any two points of the moduli space may be linked by a chain of twistor lines.

A reference where this is nicely explained (and used !) is Huybrecht's Bourbaki talk about Verbitsky's Torelli theorem : http://arxiv.org/abs/1106.5573. More precisely, Definition 3.3 gives a lattice-theoretic definition of twistor lines, the link with your description of twistor lines is made in paragraph 4.4, and the result I mentionned above is Proposition 3.7.

In the polarized case, no twistor line is included in the moduli space, as a general member is not projective : see remark 8.1 of http://arxiv.org/abs/1009.0413. This article is particularly interesting in this respect. Indeed, Charles and Markman prove the standard conjectures for some projective hyperkähler varieties (a statement peculiar to projective varieties) using deformations along a twistor line (hence using non-projective varieties).

These $2$-spheres are called 'twistor lines'. They indeed cover the moduli space : more precisely, any two points of the moduli space may be linked by a chain of twistor lines.

A nice reference where this is explained (and used !) is Huybrecht's Bourbaki talk about Verbitsky's Torelli theorem : the http://arxiv.org/pdf/1106.5573v1.pdf. See particularly paragraphs 3.2 and 4.4.

These $2$-spheres are called 'twistor lines'. They indeed cover the moduli space (in the non-polarized case) : more precisely, any two points of the moduli space may be linked by a chain of twistor lines.

A reference where this is nicely explained (and used !) is Huybrecht's Bourbaki talk about Verbitsky's Torelli theorem : http://arxiv.org/abs/1106.5573. See particularly paragraphs 3.2 and 4.4.

In the polarized case, no twistor line is included in the moduli space, as a general member is not projective : see remark 8.1 of http://arxiv.org/abs/1009.0413. This article is particularly interesting in this respect. Indeed, Charles and Markman prove the standard conjectures for some projective hyperkähler varieties (a statement peculiar to projective varieties) using deformations along a twistor line (hence using non-projective varieties).