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We give a new and intrinsic proof of the transitivity of the braid groupaction on the set of full exceptional sequences of coherent sheaves on aweighted projective line. We do not use here the corresponding result ofCrawley-Boevey for modules over hereditary algebras. As an application we provethat the strongest global dimension of the category of coherent sheaves on aweighted projective line $\XX$ does not depend on the parameters of $\XX$.Finally we prove that the determinant of the matrix obtained by taking thevalues of $n$ $\ZZ$-linear functions defined on the Grothendieck group$K_0(\XX) \simeq \ZZ^n $ of the elements of a full exceptional sequence is aninvariant, up to sign.

The braid group action on exceptional sequences for weighted projective lines