Por que "ing" após "to"?

Hi, there!

Could you please, tell me why grammatically after "to" there is "having", instead of "have", in the sentence below.

"There are many advantages to having a rich English vocabulary."

Thanks in advance!

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There's a lot of type of sentences in which the verb that comes after the preposition to is put into the gerund form.

Look forward to...
Addicted to...
I'm used to...
Confessed to...
Close to...
New to...
Prior to...
Advantages to...
Secrets to...

Well I'm not going to mention all of them because I could go on pretty much forever. You get the hang of it as you get more and more exposure to English, after a while knowing whether or not to use "ing" will be natural for you.

In some cases using gerund is necessary for you to convey the idea that you intend to:

He confessed to kill her = he made a confession in order to kill her
He confessed to killing her = he confessed that he's the one who killed her.

It might be that you'll still get your point across even if you don't use ing because more likely than not the context leading up to it will make it obvious,seeing as the context of confessing someting in order to kill someone is far more unlikely than the other one. But if you were to say that one made a confession so that they could kill somebody, "kill" would be in the neutral form, as opposed to confessing to doing something in the sense that you're the culprit which is always in the gerund form.
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After a preposition usually we use the gerund, after certain verbs and after some express like "can´t stand/it´s worth".