In غُلَامِي, غُلَام: noun and first term of iḍāfa; ي: first-person possessive pronoun, in the genitive position.
The kasra on mīm is the vowel of phonetic compatibility required before the possessive yāʾ. It appears in all three cases, not just the genitive.
The noun’s actual case vowel is therefore estimated: ḍamma, fatḥa or kasra according to function.
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Noun Case Class 7 — Maqṣūr and Nouns with Possessive Yāʾ
In غُلَامِي, غُلَام: noun and first term of iḍāfa; ي: first-person possessive pronoun, in the genitive position.
The kasra on mīm is the vowel of phonetic compatibility required before the possessive yāʾ. It appears in all three cases, not just the genitive.
The noun’s actual case vowel is therefore estimated: ḍamma, fatḥa or kasra according to function.