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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
##### Keywords:
Picard group; divisor classes; Severi variety
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