there be 句型的就近原则就近的是后面所跟的名词性成分
就你所说的题应该用there are
这里的there are修饰的是books而不是a variety of
a variety of 则是另一个修饰books的词组
还原回来
你也可以这样理解
a variety of books are there
你不可能说a variety of books is there 吧
而且……there be句型的就近原则应该是更体现在有两者以上
比如：there is some milk and books on the table
there are some books and milk on the table