The generators of the group birational automorphisms any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to projective plane are explicitly described.

This preprint supersedes the previous version, which was only about Kontsevich's conjecture on relation between monodromy of a family (weakly) CY varieties and action cohomology group autoequivalences derived category in mirror dual family. Here we add another autoequivalence variety its Neron-Severi Lie algebra.

We show the boundedness of finite subgroups in any anisotropic reductive algebraic group over a perfect field that contains all roots 1. Also, we provide explicit bounds for orders automorphism groups Severi-Brauer varieties and quadrics such fields.

We study parameter spaces of linear series on projective curves in the presence unibranch singularities, i.e. cusps; and to do so, we stratify cusps according value semigroup. show that generalized Severi varieties maps P1→Pn with images fixed degree arithmetic genus are often reducible whenever n≥3. also prove variety degree-d a hyperelliptic cusp delta-invariant g≪d is codimension at least (n...

Continuing the work of Chiantini and Ciliberto (1999) on the Severi varieties of curves on surfaces in P3, we complete the proof of the existence of regular components for such varieties. 2000 Mathematics Subject Classification. 14H10, 14B07.

We classify finite groups that can act by automorphisms and birational on non-trivial Severi–Brauer surfaces over fields of characteristic zero.