Can we say:
- His swimming is brilliant
I made up this sentence to examine:
1) if i can use possessive adjectives before gerund.
2) and if a gerund can stand by its own without an object.
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His swimming is brilliant.
Although the word swimming is a gerund, it's best to call its grammatical use here a noun or gerund noun.
That makes everything easier. Just like you can say: "My car is nice.", you can say: "But my driving is lousy." Car and driving are nouns.
As for a noun without an object, bear in mind that verbs have objects (He played the song.), not nouns. Nouns don't have objects.
Most nouns can take possessives. And gerunds used as nouns (not adjectives) can also.
Reminder: gerunds can be nouns or adjectives.