By Ragnar Benson

Do you've gotten a weapon on your arsenal that may carry off tanks or a small military of antagonistic humans? What you would like is a flamethrower. They're affordable; effortless to construct and hold; and use universal, reasonably cheap gas. A recipe for napalm is integrated. One whiff of the dragon"s breath will placed attackers at your mercy.

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26] J. Itard, Lagrange, Joseph Louis, in Dictionary of Scientific Biography, VII, Scribner’s Sons, New York, 1975, 559–573. [27] S. L’Huillier, Exposition ´el´ementaire des principes des calculs sup´erieure, Decker, Berlin, 1787. L. Lagrange, Th´eorie des fonctions analytiques, Impr. de la R´epublique, Paris, 1797. [29] A. Lomholt, Det Kongelige Danske Videnskabers Selskab, 1749–1942, I kommission hos E. Munksgaard, Copenhagen, 1942. [30] J. L¨ utzen, Joseph Liouville 1809–1882, Master of Pure and Applied Mathematics, Springer-Verlag, New York, 1990.

That Chern classes are algebraic cycles holds, basically, because vector bundles have plenty of meromorphic sections. (iii) A particular case of (ii) is that the integral linear combinations of classes of divisors (= codimension 1 cycles) are simply the first Chern classes of line bundles. If Z + − Z − is the divisor of a meromorphic section of L, c1 (L) = cl(Z + ) − cl(Z − ). This is the starting point of the proof given by Kodaira and Spencer [7] of the Hodge conjecture for H 2 : a class c ∈ H 2 (X, Z) of type (1, 1) has image 0 in the quotient H 0,2 = H 2 (X, O) of H 2 (X, C), and the long exact sequence of cohomology defined by the exponential exact sequence exp(2πi ) 0 −−−−→ Z −−−−→ O −−−−−−−→ O∗ −−−−→ 0 shows that c is the first Chern class of a line bundle.

To express cl(Z) in terms of Chern classes, one resolves the structural sheaf OZ by a finite complex of vector bundles. That Chern classes are algebraic cycles holds, basically, because vector bundles have plenty of meromorphic sections. (iii) A particular case of (ii) is that the integral linear combinations of classes of divisors (= codimension 1 cycles) are simply the first Chern classes of line bundles. If Z + − Z − is the divisor of a meromorphic section of L, c1 (L) = cl(Z + ) − cl(Z − ).