1,398 research outputs found
Convexity preserving interpolatory subdivision with conic precision
The paper is concerned with the problem of shape preserving interpolatory
subdivision. For arbitrarily spaced, planar input data an efficient non-linear
subdivision algorithm is presented that results in limit curves,
reproduces conic sections and respects the convexity properties of the initial
data. Significant numerical examples illustrate the effectiveness of the
proposed method
A bit of tropical geometry
This friendly introduction to tropical geometry is meant to be accessible to
first year students in mathematics. The topics discussed here are basic
tropical algebra, tropical plane curves, some tropical intersections, and
Viro's patchworking. Each definition is explained with concrete examples and
illustrations. To a great exten, this text is an updated of a translation from
a french text by the first author. There is also a newly added section
highlighting new developments and perspectives on tropical geometry. In
addition, the final section provides an extensive list of references on the
subject.Comment: 27 pages, 19 figure
Stable pair compactification of moduli of K3 surfaces of degree 2
We prove that the universal family of polarized K3 surfaces of degree 2 can
be extended to a flat family of stable slc pairs over the
toroidal compactification associated to the Coxeter fan. One-parameter
degenerations of K3 surfaces in this family are described by integral-affine
structures on a sphere with 24 singularities.Comment: v2: Updated reference
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