Some remarks on the Severi varieties of surfaces inℙ3
نویسندگان
چکیده
منابع مشابه
Some Remarks on the Severi Varieties of Surfaces in P3
Continuing the work of Chiantini and Ciliberto (1999) on the Severi varieties of curves on surfaces in P3, we complete the proof of the existence of regular components for such varieties. 2000 Mathematics Subject Classification. 14H10, 14B07.
متن کاملSome Remarks on the Severi Varieties of Surfaces in P
Continuing the work of Chiantini and Ciliberto on the Severi varieties of curves on surfaces in P, we complete the proof of the existence of regular components for such varieties. 2000 Mathematics Subject Classification. Primary 14H10, 14B07
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In the current paper we prove that any Severi variety on a Hirzebruch surface contains a unique component parameterizing irreducible nodal curves of the given genus in characteristic zero.
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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 ...
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0.1 Notations. We deal in this paper with complex projective K3 surfaces, i.e. smooth K-trivial complex projective surfaces without irregularity. Let φ : S 99K S be a dominant self rational map. Suppose Pic(S) = Z. Then there exists a positive integer l such that φOS(1) ∼= OS(l). It is the algebraic degree of φ, that is the degree of the polynomials defining φ. There always exists an eliminatio...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2001
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171201020178