Phylogenetic Algebraic Geometry

Abstract

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.

15 pages, 7 figures

References in corpus (1)

• Higher secant varieties of Segre-Veronese varieties

Cited by in corpus (16)

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• Implicit inequality constraints in a binary tree model
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• Four lectures on secant varieties
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• Phylogenetic ideals and varieties for the general Markov model
• Grassmann secants, identifiability, and linear systems of tensors
• On phylogenetic trees - a geometer's view
• Finite phylogenetic complexity and combinatorics of tables
• Phylogenetics of Indo-European Language families via an Algebro-Geometric Analysis of their Syntactic Structures
• Complete intersection for equivariant models
• H-Representation of the Kimura-3 Polytope
• Conformal blocks, Berenstein-Zelevinsky triangles and group-based models
• On the ideals of equivariant tree models