Minimal families of curves on surfaces
See my research statement for an overview of my research on minimal families.
During my PhD I started to do research on minimal families.
PhD thesis: "Minimal families of curves on surfaces", 2011
advisor: Josef Schicho, examiner: Gavin Brown.
Johannes Kepler University, Linz, Austria,
See section 2.3 in  for the main contributions.
The following articles contain the content of my PhD thesis.
with Josef Schicho, "Lattice polygons and families of curves on rational surfaces"
Journal of Algebraic Combinatorics, Springer, page 1-24, 2010,
"Algorithms for singularities and real structures of weak Del Pezzo surfaces"
Journal of Algebra and its Applications, World Scientific, 2013,
"Families of bitangent planes of space curves and minimal non-fibration families"
"Minimal families of curves on surfaces"
"A degree bound for families of rational curves on surfaces"
The following articles improve, extend and/or correct the following parts of my thesis:
- For sections C.4 until C.7 in  see instead .
- For section 6.2 and sections 8.6 until 8.11 in  see instead  (in particular the proof of proposition 76 in section 6.2 is incorrect in ).
- For section 4.3 in  see instead  (there is a gap in proposition 26 of , this is fixed and simplified in ).
Implementation of algorithms (work in progress)
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
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.
Examples of minimal families