Question

A pronoun preceding a gerund is in the _______ case?

Answer 1

A pronoun preceding a gerund is in the possesive case. Because a gerund functions like that of a noun, we use the possessive case of nouns to modify it. An example is, " My sister's swimming to the beach resulted to itches around her body." A gerund is a noun with an addition of -ing

Answer 2

A pronoun preceding a gerund is in the 1. possessive case. 
For example: 
I appreciate you taking time to talk with me about the project.