Errors in my firebase delete account code in my flutter app - flutter

Question

I have created a delete account page in my Flutter app . And I have written a code for the onPressed function.
My logic: On the delete account page I have added 2 text fields, they are: email and password, when the user enters his email and password and clicks on the Delete Account button, I want firebase to check whether the credentials are correrct. Only if the credentials are correct I want firebase to delete the account.
But I'm getting an error:
The method 'delete' isn't defined for the type 'AuthUser'.
Try correcting the name to the name of an existing method, or defining a method named 'delete'.
onPressed code:
onPressed: () async {
final email = _email.text;
final password = _password.text;
try {
await AuthService.firebase().logIn(
email: email,
password: password,
);
final user = AuthService.firebase().currentUser;
await user?.delete();
} on UserNotFoundAuthException {
await showErrorDialog(
context,
'User not found',
);
} on WrongPasswordAuthException {
await showErrorDialog(
context,
'Wrong credentials',
);
} on GenericAuthException {
await showErrorDialog(
context,
'Authentication error',
);
}