Points in Projective Spaces and Applications
نویسنده
چکیده
Abstract. We prove that points of a finite subset Σ ⊂ P impose independent linear conditions on homogeneous forms on P of degree ⌊nλ/2 − n⌋ in the case when at most λk points of the set Σ lie on a possibly reducible curve in P of degree k and |Σ| < λ⌈λ/2⌉, where λ is a natural number and n > 3. We apply the obtained result to threefolds having at most isolated ordinary double points. In particular, we prove the factoriality of a double cover of P branched over a nodal surface of degree 2r less than (2r− 1)r nodes. On the other hand, there are non-factorial double covers of P branched over a nodal surface of degree 2r with (2r − 1)r nodes.
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