Fenerator light - problem?

[Heckler]

Hallo,

fixed the indicator problem from yesterday.
last week I charged up the battery and when I connected it the +ve cable immediately got extremely hot and I quickly disconnected it. It now has a shrivelled outer. Checked the battery and think that it had a short. Replaced it, but now when I connected the new battery the generator light is on with the ignition key in the off position When I turn the key , the light goes out in the horizontal position (where it normally comes on) and the engine starts as normal, generator light off.

Any ideas what is wrong?

Thanks

What type of Alfa do you have?

[Heckler]

Sorry, should have said. It's a European 1973 2.0l 105 Kammtail.