The dimension growth conjecture
For any n≥3, let V⊂ℙn−1 be an irreducible variety of degree d whose ideal is generated by forms defined over the rationals. In this degree of generality one might still ask whether anything meaningful can be said about the corresponding counting function N v (B), as defined in (1.6). In contrast to the preceding chapter, where precise asymptotic formulae were sought for N U (B) for suitable open subsets U⊆V, the aim of the present chapter is to seek general upper bounds for the full counting function N V (B), making as few assumptions on V as possible.
KeywordsLinear Space Irreducible Component Singular Locus Hyperplane Section Fano Variety
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