Given a partition (d1,...,dr) of d, we consider the variety X parameterizing forms F of degree d in k[x_0,x_1,x_2], which are the product of r forms F1,...,Fr of degree d1,...,dr, respectively. We study the secant line variety X, and we determine, for all r and d$, whether or not such a secant variety is defective. Defectivity occurs in infinitely many ``unbalanced" cases.
The secant line variety to the varieties of reducible plane curves
CATALISANO, MARIA VIRGINIA;GERAMITA, ANTHONY VITO;
2016-01-01
Abstract
Given a partition (d1,...,dr) of d, we consider the variety X parameterizing forms F of degree d in k[x_0,x_1,x_2], which are the product of r forms F1,...,Fr of degree d1,...,dr, respectively. We study the secant line variety X, and we determine, for all r and d$, whether or not such a secant variety is defective. Defectivity occurs in infinitely many ``unbalanced" cases.
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