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- W1978511673 abstract "Let X, Y be smooth complex projective varieties of dimension n≥2 and let f: Y→X be a totally ramified abelian cover. Assume that the components of the branch divisor of f are ample. Then the map f*: π1(Y)→π1(X) is surjective and gives rise to a central extension: begin{equation} 0 to K to pi_1 (Y)to pi_1(X) to 1 end{equation} where K is a finite group. Here we show how the kernel K and the cohomology class c(f) ∈ H2(π1(X), K) of (1) can be computed in terms of the Chern classes of the components of the branch divisor of f and of the eigensheaves of $f_*{mathcal O}_Y$ under the action of the Galois group. Using this result, for any integer m>0, we construct m varieties X1,…, Xm no two of which are homeomorphic, even though they have the same numerical invariants and they are realized as covers of the same projective variety X with the same Galois group, branch locus and inertia subgroups." @default.
- W1978511673 created "2016-06-24" @default.
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- W1978511673 date "1995-10-01" @default.
- W1978511673 modified "2023-09-25" @default.
- W1978511673 title "ON THE FUNDAMENTAL GROUP OF AN ABELIAN COVER" @default.
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- W1978511673 doi "https://doi.org/10.1142/s0129167x9500033x" @default.
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