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Formally, a rational map: between two varieties is an equivalence class of pairs (,) in which is a morphism of varieties from a non-empty open set to , and two such pairs (,) and (′ ′, ′) are considered equivalent if and ′ ′ coincide on the intersection ′ (this is, in particular, vacuously true if the intersection is empty, but since is assumed irreducible, this is impossible).
A birational map from X to Y is a rational map f : X ⇢ Y such that there is a rational map Y ⇢ X inverse to f.A birational map induces an isomorphism from a nonempty open subset of X to a nonempty open subset of Y, and vice versa: an isomorphism between nonempty open subsets of X, Y by definition gives a birational map f : X ⇢ Y.
If X is a smooth complete curve (for example, P 1) and if f is a rational map from X to a projective space P m, then f is a regular map X → P m. [5] In particular, when X is a smooth complete curve, any rational function on X may be viewed as a morphism X → P 1 and, conversely, such a morphism as a rational function on X.
The largest living land animal, the African bush elephant, is a herbivore. This is a list of herbivorous animals, organized in a roughly taxonomic manner. In general, entries consist of animal species known with good certainty to be overwhelmingly herbivorous, as well as genera and families which contain a preponderance of such species.
Various carnivorans, with feliforms to the left, and caniforms to the right. Carnivora is an order of placental mammals that have specialized in primarily eating flesh. Members of this order are called carnivorans, or colloquially carnivores, though the term more properly refers to any meat-eating organisms, and some carnivoran species are omnivores or herbivores.
Lions are obligate carnivores consuming only animal flesh for their nutritional requirements.. A carnivore / ˈ k ɑːr n ɪ v ɔːr /, or meat-eater (Latin, caro, genitive carnis, meaning meat or "flesh" and vorare meaning "to devour"), is an animal or plant whose nutrition and energy requirements are met by consumption of animal tissues (mainly muscle, fat and other soft tissues) as food ...
Many civilizations have incorporated a species of carnivoran into their culture: a prominent example is the lion, viewed as a symbol of power and royalty in many societies. Yet many species such as wolves and the big cats have been broadly hunted, resulting in extirpation in some areas.
Examples of mono-gastric omnivores include humans hamsters and rats. Furthermore, there are monogastric carnivores such as cats . [ 1 ] A monogastric organism is contrasted with ruminant organisms (which have four-chambered complex stomachs), such as cattle , goats , and sheep .