Check this out from Wallace's Greek Grammar Beyond the Basics (amazon.com): p. 79-81.
No, first you need background. I was looking at James 2.1:
Ἀδελφοί μου, μὴ ἐν προσωπολημψίαις ἔχετε τὴν πίστιν τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ τῆς δόξης. (NA27)
My brothers, show no partiality as you hold the faith in our Lord Jesus Christ, the Lord of glory. (ESV)
My brothers and sisters, do you with your acts of favoritism really believe in our glorious Lord Jesus Christ? (NRSV)
Confused about τῆς δόξης and what it modifies, I went to the Lexham Syntactic Greek New Testament. It notes that δόξης is a "Descriptive Genitive" and cites Wallace pp. 79-81. The Lexham SGNT cleared up the modification issue for me, but it provoked a different question. What in the world is a "descriptive genitive"? (I mean, aren't all genitives descriptive?) I went to read the pages cited in Wallace. Here's what I found, which I quote verbatim. This text is really in there!
†1. Descriptive Genitive (“Aporetic” Genitive21) [characterized by, described by]
a. Definition
The genitive substantive describes the head noun in a loose manner. The nature of the collocation of the two nouns in this construction is usually quite ambiguous.
b. Amplification
This is the “catch-all” genitive, the “drip pan” genitive, the “black hole” of genitive categories that tries to suck many a genitive into its grasp! In some respects, all adjectival genitives are descriptive, yet no adjectival genitive is descriptive. That is to say, although all adjectival genitives are, by their nature, descriptive, very few, if any, belong only to this specific category of usage. This use truly embodies the root idea of the (adjectival) genitive. It is often the usage of the genitive when it has not been affected by other linguistic considerations-that is, when there are no contextual, lexemic, or other grammatical features that suggest a more specific nuance.22
Frequently, however, it is close to the attributive genitive, being either other than or broader than the attributive use.23 (See chart 7 below.) Hence, this use of the genitive should be a last resort. If one cannot find a narrower category to which a genitive belongs, this is where he or she should look for solace.24
Further, some footnotes are worthy of evaluation as well:
Note 21: That is, the “I am at a loss” gen. (from the Greek word, ἀπορέω, “I am at a loss,” a tongue-in-cheek title suggested to me by J. Will Johnston). This is the category one should appeal to when another slot cannot be found. The title is descriptive not of the gen., but of the feeling one has in the pit of his/her stomach for having spent so much time on this case and coming up with nothing.
Note 24: Since there is already a plethora of gen. categories, we had to stop somewhere. The descriptive gen. covers a multitude of syntactical categories which have, as yet, to receive published sanction (though this would be a worthy project). It seems that one of the chief situations in which descriptive genitives occur is when either the head noun or the gen. noun is highly idiomatic, figurative, or informed by Semitic usage. Thus, υἱός + noungen is perhaps frequently descriptive (e.g., “son of disobedience”). To call this merely attributive (“disobedient son”) is not adequate, for “son” then does not get interpreted. (υἱός with gen. is notoriously complex; see Zerwick, Biblical Greek, 15–16 [§42–43] for summary of uses.) Also, when the head noun is figurative, such as in “root of bitterness” (ῥίζα πικρίας, Heb 12:15), the gen. can frequently be described as descriptive.
At the same time, our approach in this chapter overall is different from grammars that refuse to analyze the descriptive gen. (e.g., Young, Intermediate Greek, 23; Moule, Idiom Book, 37), because we believe that such analysis is not intuitive with most students of Greek and, further, that the additional categories have exegetical value.