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Every irreducible complex algebraic curve is birational to a unique smooth projective curve, so the theory for curves is trivial. The case of surfaces was first investigated by the geometers of the Italian school around 1900; the contraction theorem of Guido Castelnuovo essentially describes the process of constructing a minimal model of any smooth projective surface.
The tree of life or universal tree of life is a metaphor, conceptual model, and research tool used to explore the evolution of life and describe the relationships between organisms, both living and extinct, as described in a famous passage in Charles Darwin's On the Origin of Species (1859).
A variety is called uniruled if it is covered by rational curves. A uniruled variety does not have a minimal model, but there is a good substitute: Birkar, Cascini, Hacon, and McKernan showed that every uniruled variety over a field of characteristic zero is birational to a Fano fiber space.
The 1735 classification of animals. Only in the Animal Kingdom is the higher taxonomy of Linnaeus still more or less recognizable and some of these names are still in use, but usually not quite for the same groups. He divided the Animal Kingdom into six classes. In the tenth edition, of 1758, these were: Classis 1. Mammalia (mammals) Classis 2 ...
Systematic biology (hereafter called simply systematics) is the field that (a) provides scientific names for organisms, (b) describes them, (c) preserves collections of them, (d) provides classifications for the organisms, keys for their identification, and data on their distributions, (e) investigates their evolutionary histories, and (f ...
The idea of a tree of life arose from ancient notions of a ladder-like progression from lower into higher forms of life (such as in the Great Chain of Being).Early representations of "branching" phylogenetic trees include a "paleontological chart" showing the geological relationships among plants and animals in the book Elementary Geology, by Edward Hitchcock (first edition: 1840).
Linnaeus's Systema Naturae lists only about 10,000 species of organisms, of which about 6,000 are plants and 4,236 are animals. [9] According to the historian of botany William T. Stearn , "Even in 1753 he believed that the number of species of plants in the whole world would hardly reach 10,000; in his whole career he named about 7,700 species ...
Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field of rational numbers has only finitely many rational points. This was conjectured in 1922 by Louis Mordell , [ 1 ] and known as the Mordell conjecture until its 1983 proof by Gerd Faltings . [ 2 ]