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There is an approach to intersection number, introduced by Snapper in 1959-60 and developed later by Cartier and Kleiman, that defines an intersection number as an Euler characteristic. Let X be a scheme over a scheme S , Pic( X ) the Picard group of X and G the Grothendieck group of the category of coherent sheaves on X whose support is proper ...
As well as being called the intersection number, the minimum number of these cliques has been called the R-content, [7] edge clique cover number, [4] or clique cover number. [8] The problem of computing the intersection number has been called the intersection number problem , [ 9 ] the intersection graph basis problem , [ 10 ] covering by ...
The Free Press (known as Common Sense between 2021–2022) is an American Internet-based media company based in Los Angeles, California, founded by Bari Weiss and Nellie Bowles. [ 1 ] [ 2 ] The newsletter was first published in 2021 [ 3 ] [ 4 ] while its associated media company officially launched in 2022.
As another example, the number 5 is not contained in the intersection of the set of prime numbers {2, 3, 5, 7, 11, …} and the set of even numbers {2, 4, 6, 8, 10, …} , because although 5 is a prime number, it is not even. In fact, the number 2 is the only number in the intersection of these two
Consider a line L in the projective plane P 2: it has self-intersection number 1 since all other lines cross it once: one can push L off to L′, and L · L′ = 1 (for any choice) of L′, hence L · L = 1. In terms of intersection forms, we say the plane has one of type x 2 (there is only one class of lines, and they all intersect with each ...
A K3 surface is compact, 4 dimensional, and () vanishes, and the signature is −16, so 16 is the best possible number in Rokhlin's theorem. A complex surface in C P 3 {\displaystyle \mathbb {CP} ^{3}} of degree d {\displaystyle d} is spin if and only if d {\displaystyle d} is even.
More generally, a line bundle L on a proper scheme X over a field k is said to be nef if it has nonnegative degree on every (closed irreducible) curve in X. [1] ( 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.)
In mathematical set theory, a pseudo-intersection of a family of sets is an infinite set S such that each element of the family contains all but a finite number of elements of S. The pseudo-intersection number , sometimes denoted by the fraktur letter 𝔭, is the smallest size of a family of infinite subsets of the natural numbers that has the ...