Search results
Results from the WOW.Com Content Network
A line bundle is ample if some positive power is very ample. An ample line bundle on a projective variety has positive degree on every curve in . The converse is not quite true, but there are corrected versions of the converse, the Nakai–Moishezon and Kleiman criteria for ampleness.
In mathematics, a positive polynomial (respectively non-negative polynomial) on a particular set is a polynomial whose values are positive (respectively non-negative) on that set. Precisely, Let p {\displaystyle p} be a polynomial in n {\displaystyle n} variables with real coefficients and let S {\displaystyle S} be a subset of the n ...
However, the degree sequence does not, in general, uniquely identify a graph; in some cases, non-isomorphic graphs have the same degree sequence. The degree sequence problem is the problem of finding some or all graphs with the degree sequence being a given non-increasing sequence of positive integers. (Trailing zeroes may be ignored since they ...
Given a homogeneous polynomial of degree with real coefficients that takes only positive values, one gets a positively homogeneous function of degree / by raising it to the power /. So for example, the following function is positively homogeneous of degree 1 but not homogeneous: ( x 2 + y 2 + z 2 ) 1 2 . {\displaystyle \left(x^{2}+y^{2}+z^{2 ...
Every univariate polynomial with real coefficients of positive degree can be factored as , where c is a real number and each is a monic polynomial of degree at most two with real coefficients. Moreover, one can suppose that the factors of degree two do not have any real root.
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer .
The degree of a line bundle L on a proper curve C over k is the degree of the divisor (s) of any nonzero rational section s of L.) A line bundle may also be called an invertible sheaf . The term "nef" was introduced by Miles Reid as a replacement for the older terms "arithmetically effective" ( Zariski 1962 , definition 7.6) and "numerically ...
The singular cohomology of a contractible space vanishes in positive degree, but the Poincaré lemma does not follow from this, since the fact that the singular cohomology of a manifold can be computed as the de Rham cohomology of it, that is, the de Rham theorem, relies on the Poincaré lemma. It does, however, mean that it is enough to prove ...