I’ve been meaning to write up some of the things that were covered during the review class on Tuesday, but I haven’t had a spare moment. However, since I was asked something over email that relates obliquely to this, let me run through one of those things here.
The only place that the genitive case ever shows up is in the specifier of DP, and more specifically, it shows up in the specifier of a DP whose head is ∅GEN. The D ∅GEN has the features [D, ucase:gen*, ucase: ] (that is, it is a D, it assigns genitive case to its specifier, and the DP it heads must itself get case).
So, if you see something in the genitive case (something like his, her, their, senator’s or Pat’s), you know that it is in SpecDP. In fact, that is the basic function of Case, to tell you where something is in the tree.
(Likewise, if you see something that is in nominative case, you know that it is in the specifier of TP.)
Meanwhile, if we consider the function of the UTAH, the UTAH tells us the θ-role that goes with a DP (or, in the case of Goal, a PP) is based on the position in which it first appeared in the tree (as it was built from the bottom up using Merge). A DP in the specifier of vP (the DP daughter of vP) or a DP in the specifier of nP (the DP daughter of nP) will be an Agent (or, sometimes, an Experiencer). The DP daughter of NP and the DP daughter of VP will be a Theme. A PP sister of N and a PP sister of V will be a Goal.
Thinking first about verbal clauses (TPs), notice that the θ-role of the nominative argument (the subject) can be one of several different possibilities:
(1) I jumped.
(2) I fell.
(3) I was pushed.
(4) I was given a book.
(5) I was introduced to Mary.
In each case above, I is of course nominative, it is the subject, it is in the specifier of TP. But it started in different places in different sentences, even though in each case it moved into the specifier of TP. In (1), I is an Agent, so it started in SpecvP. In (2-5), I is a Theme, so it started in SpecVP. In (2), we have an unaccusative verb, in (3) we have a passive transitive verb, in (4) we have the passive of a ditransitive verb (of the “have” type, it was caused to be that I had a book), and in (5) we have the passive of a ditransitive verb (of the “go” type, it was caused that an introduction of me went to Mary).
The point here is that: Case tells you where a DP ends up, and the θ-role tells you where that DP started out.
The same is true in DPs. So, we have several possibilities:
(6) [My hat] was ugly.
(7) [My buying of a hat] was a mistake.
(8) [My falling] was painful.
In each case (6-8), my is genitive, meaning that it is in SpecDP. In (6), my is the possessor of the hat (it has a Possessor θ-role). In (7), my is the agent of the buying event (it has an Agent θ-role). In (8), my is the theme of the (unaccusative) falling event (it has a Theme θ-role). So, my started out in a different place in each of the three examples in (6-8).
Starting first with (7), we know that because my is getting the Agent θ-role, it must have started in SpecnP. In (8), we know that my started as the DP daughter of NP (in this case the sister of N), since it is getting the Theme θ-role.
In (6), because my is a Possessor, we know that it started in the specifier of a PossP. Because it is not Agent or Theme, it couldn’t have started as DP daughter of nP or DP daughter of NP. Because there is a Possessor θ-role assigned, there must have been a PossP in whose specifier my was first Merged.
The Hierarchy of Projections within the DP goes like this: D > (Poss >) n > N. So, the PossP was between n and D.
This also means, incidentally, that the only time you need a PossP is when you have something that gets a Possessor θ-role (the Poss is optional in the HoP for the DP, just like Pass, Perf, Prog, Neg, and M are in the HoP for the TP).
Anyway, the strategy for deciding what the tree should look like when you are drawing a DP is to first determine the θ-role of the genitive DP. If it is a Possessor, you need a PossP, and the Possessor starts in SpecPossP, then moves to SpecDP. If it is an Agent, you don’t need a PossP, and the DP starts in SpecnP, then moves to SpecDP. If it is a Theme, you don’t need a PossP, and the DP starts as the DP daughter of NP, and moves to SpecDP.