arXiv subjects

Holger Partsch

Publications and source records attributed to Holger Partsch.

2 recordsLinked to original sources

arXiv2011

Deformations of elliptic fibre bundles in positive characteristic

We study deformation theory of elliptic fibre bundles over curves in positive characteristics. As applications, we give examples of non-liftable elliptic surfaces in charactertic two and three, which answers a question of Katsura and Ueno. Also, we construct a class of elliptic fibrations, whose liftability is equivalent to a conjecture of F. Oort concerning the liftability of automorphisms of curves. Finally, we classify deformations of bielliptic surfaces.

math.AG↗

arXiv2008

Quotient categories, stability conditions, and birational geometry

This article deals with the quotient category of the category of coherent sheaves on an irreducible smooth projective variety by the full subcategory of sheaves supported in codimension greater than c. It turns out that this category has homological dimension c. As an application of this, we will describe the space of stability conditions on its derived category in the case c=1. Moreover, we describe all exact equivalences between these quotient categories in this particular case which is closely related to classification problems in birational geometry.

math.AG↗