On the Severi Varieties of Surfaces in P
نویسنده
چکیده
For a smooth surface S in P 3 of degree d and for positive integers n, δ, the Severi variety V 0 n,δ (S) is the subvariety of the linear system |O S (n)| which parametrizes curves with δ nodes. We show that for S general, n ≥ d and for all δ with 0 ≤ δ ≤ dim(|O S (n)|), then V 0 n,δ (S) has at least one component which is reduced, of the expected dimension dim(|O S (n)|) − δ. We also construct examples of reducible Severi varieties on general surfaces of degree d ≥ 8.
منابع مشابه
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