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Geometry of Severi varieties. II: Independence of divisor classes and example. (English) Zbl 0677.14004
Algebraic geometry, Proc. Conf., Sundance/Utah 1986, Lect. Notes Math. 1311, 23-50 (1988).
In this sequel to part I of this paper [Trans. Am. Math. Soc. 309, No. 1, 1–34 (1988; Zbl 0677.14003)], the authors establish the linear independence, over \(\mathbb Q\), of their intrinsic divisor classes A, B, C and \(\Delta\). For the proof, the authors construct a restriction homomorphism from \(\operatorname{Pic}(W(d,\delta))\) to \(\operatorname{Pic}(W(d,\delta-1))\), where \(W(d,\delta)\) denotes the Severi variety (in the author’s sense) of plane curves of degree \(d\) which are singular at exactly \(\delta\) nodes. The restriction homomorphism reduces the verification of independence to small values of the genus \(g\); the conclusion follows by inspecting five explicit families of curves. The paper concludes with a series of useful examples.
[For the entire collection see Zbl 0635.00006.]

MSC:
14H10 Families, moduli of curves (algebraic)
14C20 Divisors, linear systems, invertible sheaves
14C22 Picard groups
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