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In macroeconomics, the guns versus butter model is an example of a simple production–possibility frontier. It demonstrates the relationship between a nation's investment in defense and civilian goods. The "guns or butter" model is used generally as a simplification of national spending as a part of GDP. This may be seen as an analogy for ...
The older terms were misleading, in view of the examples below. Every line bundle L on a proper curve C over k which has a global section that is not identically zero has nonnegative degree. As a result, a basepoint-free line bundle on a proper scheme X over k has nonnegative degree on every curve in X; that is, it is nef. [3]
1.1.1.7 Curve families of variable degree. ... This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, ...
The price of a butter slab has spiked 26% since December, reflecting how inflation is unraveling for the average Russian in Vladimir Putin's war economy. The great Russian butter robbery—and ...
For an example where "ample" and "very ample" are different, let X be a smooth projective curve of genus 1 (an elliptic curve) over C, and let p be a complex point of X. Let O(p) be the associated line bundle of degree 1 on X. Then the complex vector space of global sections of O(p) has dimension 1, spanned by a section that vanishes at p. [21]
In particular, if d = 1 (for example, if F = Q and D ⊗ R ≅ M 2 (R)), fixing a sufficiently small arithmetic subgroup of D ×, one gets a Shimura curve, and curves arising from this construction are already compact (i.e. projective). Some examples of Shimura curves with explicitly known equations are given by the Hurwitz curves of low genus:
A canonical curve of genus g always sits in a projective space of dimension g − 1. [3] When C is a hyperelliptic curve, the canonical curve is a rational normal curve, and C a double cover of its canonical curve. For example if P is a polynomial of degree 6 (without repeated roots) then y 2 = P(x)
The second potential problem is that even if the intersection is zero-dimensional, it may be non-transverse, for example, if V is a plane curve and W is one of its tangent lines. The first problem requires the machinery of intersection theory, discussed above in detail, which replaces V and W by more convenient subvarieties using the moving lemma.