Enrica Lexie -place of shooting and place of death

In Enrica Lexie case let us take an imaginary situation. Let one of the fishermen was standing near the edge of the boat and one shot hit him on his legs and he falls down to the sea and is drowned. His death has occurred in the sea. Then which court has jurisdiction to indict? India or Italy. India cannot as the death occurred in the sea. India has no jurisdiction on international waters. It is Italian courts which can take up the case. That means the country in whose jurisdiction was the perpetrator of the crime was standing is the country which has to try the case. Since it is the position of jurisdiction, the jurisdiction cannot shift if the victim was in some other place. It is the place where the crime was initiated which is more important than where its result occurred.
That means Italy has to take up this case and not India.