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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. In this ...
In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0 , this was proved by Heisuke Hironaka in 1964; [ 1 ] while for varieties of dimension at least 4 over ...
The transcendence degree of the fraction field of R, minus one; i.e. , where t is the number of algebraically independent generators one can find. The rate of growth of the plurigenera: that is, the smallest number κ such that P d / d κ {\displaystyle P_{d}/d^{\kappa }} is bounded.
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 linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles.. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.
Critical Role is an American web series in which a group of professional voice actors play Dungeons & Dragons with Mercer as the Dungeon Master and creator of the world Exandria. [2] A number of licensed works based on the show have been created, such as the Critical Role: Tal'Dorei Campaign Setting and Critical Role: Vox Machina Origins .
Heather Locklear is opening up about her favorite memories from filming the sitcom Spin City — and sharing what was different about working with Michael J. Fox versus his replacement in the ...
Expedition to the Barrier Peaks is a 1980 adventure module for the Advanced Dungeons & Dragons role-playing game written by Gary Gygax.While Dungeons & Dragons (D&D) is typically a fantasy game, the adventure includes elements of science fiction, and thus belongs to the science fantasy genre. [1]