In this case, the noun phrase a fragment [of text] can be modified attributively:
a short fragment
an isolated fragment
a Jane Austen fragment
However, it cannot be modified by a possessive determiner for two reasons:
- First, it contains the determiner a, which occupies the central determiner slot. The possessive determiner occupies the same slot, so the two cannot go together:
Jane Austen's fragment
*a Jane Austen's fragment
- Second, the repaired phrase Jane Austen's fragment conveys the wrong meaning (a fragment that belongs to Jane Austen).
Because the the above are ungrammatical and infelicitous respectively, the only recourse left to the reader is to reinterpret the phrase as [a Jane Austen]'s fragment. This has the same problem as 2 above, but has the additional problem of converting Jane Austen to a common noun, which is only felicitous in specific contexts (see here for details).
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