In Shakespeare's Hamlet, exactly what causes the death of each of these characters: Gertrude, Claudius, Laertes, Hamlet?

In
Shakespeare's , the deaths of all of theyou mention are the result of '
murderous conniving.

Claudius talksinto killingto avenge ' death. They
arrange for a friendly game of "sword play," but Laertes poisons
the tip of one sword as part of the their plan to dispose of Hamlet.

As a
backup plan, Claudius also has wine at the event, and allegedly drops a large pearl in the cup
to show his faith in Hamlet's abilities to win, saying he will have the pearl as a reward: the
pearl, however, is also poisonous.

KING:

Stay, give me drink. Hamlet, this
pearl is thine;

Here's to thy health.

Drum,
trumpets, and shots. A piece goes off.

Give him the cup.
(V.ii.283-285)

As the sword play begins, Hamlet acts
lighthearted, even though he expects treachery from some source. Laertes loses his sense of
"play" and becomes aggressive with Hamlet, drawing blood with the poisoned
sword.

In a scuffle, the swords are exchanged and Hamlet, unknowingly, ends
up with the envenomed...