Mathematics – Algebraic Geometry
Scientific paper
2004-07-02
Mathematics
Algebraic Geometry
15 pages, 7 figures
Scientific paper
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover classical geometric objects, such as toric and determinantal varieties and their secant varieties, but larger trees lead to new and largely unexplored territory. This paper gives a self-contained introduction to this subject and offers numerous open problems for algebraic geometers.
Eriksson Nicholas
Ranestad Kristian
Sturmfels Bernd
Sullivant Seth
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