Persistent URL of this record https://hdl.handle.net/1887/63084
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Arakelov inequalities and semistable families of curves uniformized by the unit ball
The main object of study in this thesis is an Arakelov inequality
which bounds the degree of an invertible subsheaf of the direct image of
the pluricanonical relative sheaf of a semistable family of curves. A natural
problem that arises is the characterization of those families for which the equality
is satisfied in that Arakelov inequality, i.e. the case of Arakelov equality.
Few examples of such families are known. In this thesis we provide some examples
by proving that the direct image of the bicanonical relative sheaf of
a semistable family of curves uniformized by the unit ball, all whose singular
fibers are totally geodesic, contains an invertible subsheaf which satisfies
Arakelov equality.
- All authors
- Damjanovic, N.
- Supervisor
- Koziarz, V.; Edixhoven, S.
- Co-supervisor
- Jong, R. de
- Committee
- Vaart, A. van der; Smit, B. de; Wentworth, R.; Roulleau, X.
- Qualification
- Doctor (dr.)
- Awarding Institution
- Institute of mathematics , Science , Leiden University
- Date
- 2018-06-14