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Assume we have a normal,connected quasi projective scheme $Y:=X/D$$Y:=X\backslash D$ where $X$ is a quasi projective scheme over field $k$, not necessarily char zero and also $D$ is a simple divisor, not necessarily connected. Then assume $W$ is ana connected etale covering of $Y$ and $C$ is a smooth connected curve inside $X$ which intersects $D$ transversally. Then can one say $W \times_X C$ is connected?

Assume we have a normal,connected quasi projective scheme $Y:=X/D$ where $X$ is a quasi projective scheme over field $k$, not necessarily char zero and also $D$ is a simple divisor, not necessarily connected. Then assume $W$ is an etale covering of $Y$ and $C$ is a smooth connected curve inside $X$ which intersects $D$ transversally. Then can one say $W \times_X C$ is connected?

Assume we have a normal,connected quasi projective scheme $Y:=X\backslash D$ where $X$ is a quasi projective scheme over field $k$, not necessarily char zero and also $D$ is a simple divisor, not necessarily connected. Then assume $W$ is a connected etale covering of $Y$ and $C$ is a smooth connected curve inside $X$ which intersects $D$ transversally. Then can one say $W \times_X C$ is connected?

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Assume we have a normal,connected quasi projective scheme $Y:=X/D$ where $X$ is a quasi projective scheme over field $k$, not necessarily char zero and also $D$ is a simple divisor, not necessarily connected. Then assume $W$ is an etale covering of $Y$ and $C$ is a smooth connected curve inside $X$ which intersects $D$ transversally. Then can one say $W \times_X C$ is connected?

Assume we have a normal,connected quasi projective scheme $Y:=X/D$ where $X$ is a projective scheme over field $k$, not necessarily char zero and also $D$ is a simple divisor, not necessarily connected. Then assume $W$ is an etale covering of $Y$ and $C$ is a smooth connected curve inside $X$ which intersects $D$ transversally. Then can one say $W \times_X C$ is connected?

Assume we have a normal,connected quasi projective scheme $Y:=X/D$ where $X$ is a quasi projective scheme over field $k$, not necessarily char zero and also $D$ is a simple divisor, not necessarily connected. Then assume $W$ is an etale covering of $Y$ and $C$ is a smooth connected curve inside $X$ which intersects $D$ transversally. Then can one say $W \times_X C$ is connected?

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Connected curve

Assume we have a normal,connected quasi projective scheme $Y:=X/D$ where $X$ is a projective scheme over field $k$, not necessarily char zero and also $D$ is a simple divisor, not necessarily connected. Then assume $W$ is an etale covering of $Y$ and $C$ is a smooth connected curve inside $X$ which intersects $D$ transversally. Then can one say $W \times_X C$ is connected?