Geodesic
Determinantal Resolution of the Universal Subscheme in $\mathscr S\times H_{d+1}$
Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 286-294.

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We construct a determinantal resolution of singularities for the universal subscheme in $\mathscr S\times H_{d+1}$ and prove that it is isomorphic to the variety of total pairs $\widetilde{\mathscr S\times H_d}$. 
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N. V. Timofeeva. Determinantal Resolution of the Universal Subscheme in $\mathscr S\times H_{d+1}$. Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 286-294. http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a11/

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