See my research statement for an overview of my research on minimal families.

During my PhD I started to do research on minimal families.

- [1]
*PhD thesis: "Minimal families of curves on surfaces"*, 2011

advisor: Josef Schicho, examiner: Gavin Brown.

Johannes Kepler University, Linz, Austria, [pdf]

See section 2.3 in [1] for the main contributions.

The following articles contain the content of my PhD thesis.

- [2],
with Josef Schicho,
*"Lattice polygons and families of curves on rational surfaces"* -
[3]
*"Algorithms for singularities and real structures of weak Del Pezzo surfaces"* -
[4]
*"Families of bitangent planes of space curves and minimal non-fibration families"* -
[5]
*"Minimal families of curves on surfaces"* -
[6]
*"A degree bound for families of rational curves on surfaces"*- preprint, 2014, [arxiv]

The following articles improve, extend and/or correct the following parts of my thesis:

- For sections C.4 until C.7 in [1] see instead [3].
- For section 6.2 and sections 8.6 until 8.11 in [1] see instead [4] (in particular the proof of proposition 76 in section 6.2 is incorrect in [1]).
- For section 4.3 in [1] see instead [6] (there is a gap in proposition 26 of [1], this is fixed and simplified in [6]).

These algorithms are implemented in Sage/Magma and are used to compute the number of minimal families on weak Del Pezzo surfaces. See chapter 8 in the thesis for more information. There is an implementation of the algorithm which analyses infinitely near base points of a given linear series in the projective plane. We also provide an implementation of computing linear series in the plane for given base points. We work over the algebraic closure of the rationals.

- 30 minute talk about minimal families on Del Pezzo surfaces (DMV 2009)
- 50 minute talk about minimal viewangles of lattice polygons and minimal (toric) families
- 20 minute talk about thesis: minimal families on surfaces
- poster presented at Gael
- We presented the problem of finding minimal families on threefolds at the Algebraic versus Analytic Geometry research meeting.