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Francesco Polizzi
Francesco Polizzi
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Let $X,Y$ be smooth algebraic surfaces and $\pi:X\to Y$ be a doubeldouble cover. Let $B\subseteq Y$ be the branch locus. We assume that $B$ is nef, big and smooth.

[1] says that $\pi_1(X)\cong\pi_1(Y)$ (See page 796). Why is it true?

[1]R.V.Gujar, B.P. Purnaprajna, On the Shafarevich conjecture for genus-2 fibrations, Math. Ann. (2009),343:791-800.

Let $X,Y$ be smooth algebraic surfaces and $\pi:X\to Y$ be a doubel cover. Let $B\subseteq Y$ be the branch locus. We assume that $B$ is nef, big and smooth.

[1] says that $\pi_1(X)\cong\pi_1(Y)$ (See page 796). Why is it true?

[1]R.V.Gujar, B.P. Purnaprajna, On the Shafarevich conjecture for genus-2 fibrations, Math. Ann. (2009),343:791-800.

Let $X,Y$ be smooth algebraic surfaces and $\pi:X\to Y$ be a double cover. Let $B\subseteq Y$ be the branch locus. We assume that $B$ is nef, big and smooth.

[1] says that $\pi_1(X)\cong\pi_1(Y)$ (See page 796). Why is it true?

[1]R.V.Gujar, B.P. Purnaprajna, On the Shafarevich conjecture for genus-2 fibrations, Math. Ann. (2009),343:791-800.

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Jun Lu
Jun Lu
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Why $\pi_1(X)\cong \pi_1(Y)$ for a double cover $\pi:X\to Y$ with a nef, smooth and big branch locus?

Let $X,Y$ be smooth algebraic surfaces and $\pi:X\to Y$ be a doubel cover. Let $B\subseteq Y$ be the branch locus. We assume that $B$ is nef, big and smooth.

[1] says that $\pi_1(X)\cong\pi_1(Y)$ (See page 796). Why is it true?

[1]R.V.Gujar, B.P. Purnaprajna, On the Shafarevich conjecture for genus-2 fibrations, Math. Ann. (2009),343:791-800.