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Let X be a Riemann surface.Then the intersection number of two closed curves on X has a simple definition in terms of an integral. For every closed curve c on X (i.e., smooth function :), we can associate a differential form of compact support, the Poincaré dual of c, with the property that integrals along c can be calculated by integrals over X:
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 ...
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
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.)
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.
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 ...
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Random article; About Wikipedia; Contact us; Contribute Help; ... is said to have the finite intersection property (FIP) if the ... CRC Press. ISBN 978-1584888666 ...