Is there a hose under the ac compressor on 2001 blazer?

Yes, there are several hoses connected to the AC compressor on a 2001 Chevy Blazer. There's the high-pressure line (usually thicker and smaller diameter) and the low-pressure line (usually thinner and larger diameter). They carry refrigerant to and from the compressor. There might also be other smaller lines for things like oil. It's not just one single hose.