What does definite and indefinite mean in past tense and present perfect respectively

I am reading the grammar book - A Comprehensive Grammar of the English Language - these days. I am confused about the meanings of definite and indefinite in Past Tense and Present Perfect.

I know that Past Tense means an action or state started and ended before now. For example:

He died.

From what I think, He died is the event die that happened at some point in the past. So what does the definite time mean here? And I think He died yesterday/last week is a definite time, which I know the exact time He died.

I know I am wrong, please help to point it out.

And Present Perfect has the meaning of INDEFINITE EVENT(S) IN A PERIOD LEADING UP TO THE PRESENT. For example:

He has died recently.

Which means, from an unspecified time(not too long from now) to now, in this period of time, the event die happened.

I think this is an indefinite event since I don't know the exact time when it happened.

Answer

A Comprehensive Grammar of the English Language (p184) expands its discussion of the use of the simple past in the following extract:

It is not necessary for the past tense to be accompanied by an overt
indicator of time. All that is required is that the speaker should be
able to count on the hearer's assumption that he has a specific time
in mind. In this respect, the past tense meaning of DEFINITE PAST time
is an equivalent, in the verb phrase, of the definite article in the
noun phrase. Just as with the definite article, so with the verb

phrase, an element of definite meaning may be recoverable from (a)
knowledge of the immediate or local situation; (b) the larger
situation of 'general knowledge'; (c) what has been said earlier in
the sentence or text; or (d) what comes later on in the same sentence
or text.

So this answers the question in your comment: Without explicit temporal adverbial, e.g yesterday/last week in He died yesterday/last week, how can I know the definite time of the event? Namely, the definite date or time when the event occurred will normally be recoverable in one or more of the four ways (a-d) outlined above. So, the utterance Byron died in Greece contains the implicit definite past reference: in the time that Byron was living in Greece.

As to your statement:

And Present Perfect has the meaning of INDEFINITE EVENT(S) IN A PERIOD
LEADING UP TO THE PRESENT

I'd be interested in where you have read this, since to me it is the time period that is indefinite, not the events themselves. Nevertheless, you are right that recently is an indefinite time expression which is often accompanied by the present perfect.

That said, the past tense is also used with recently. In fact, Google returns about six times more results for He died recently than He has died recently.

The choice between simple past and present perfect is very complex. For a full account of this grammar issue I recommend the excellent canonical post by StoneyB on the English Language Learners site:

https://ell.stackexchange.com/questions/13255/canonical-post-2-what-is-the-perfect-and-how-should-i-use-it