Geodesic
Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths $\ge2$ and $\ge4$ in Algebraic Surfaces
Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 743-752.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that the varieties $X_{d_1d_2}$ of complete pairs of zero-dimensional subschemes of lengths $d_1\ge2$, $d_2\ge4$ on a smooth irreducible projective algebraic surface are singular. 
@article{MZM_2003_73_5_a10,
     author = {N. V. Timofeeva},
     title = {Varieties of {Complete} {Pairs} of {Zero-Dimensional} {Subschemes} of {Lengths} $\ge2$ and $\ge4$ in {Algebraic} {Surfaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {743--752},
     publisher = {mathdoc},
     volume = {73},
     number = {5},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a10/}
}
TY  - JOUR
AU  - N. V. Timofeeva
TI  - Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths $\ge2$ and $\ge4$ in Algebraic Surfaces
JO  - Matematičeskie zametki
PY  - 2003
SP  - 743
EP  - 752
VL  - 73
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a10/
LA  - ru
ID  - MZM_2003_73_5_a10
ER  - 
%0 Journal Article
%A N. V. Timofeeva
%T Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths $\ge2$ and $\ge4$ in Algebraic Surfaces
%J Matematičeskie zametki
%D 2003
%P 743-752
%V 73
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a10/
%G ru
%F MZM_2003_73_5_a10
N. V. Timofeeva. Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths $\ge2$ and $\ge4$ in Algebraic Surfaces. Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 743-752. http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a10/

[1] Tikhomirov A. S., “Mnogoobrazie polnykh par nulmernykh podskhem algebraicheskoi poverkhnosti”, Izv. RAN. Ser. matem., 61:6 (1997), 153–180 | MR | Zbl

[2] Timofeeva N. V., “Gladkost i eilerova kharakteristika mnogoobraziya polnykh par $X_{23}$ nulmernykh podskhem dliny 2 i 3 algebraicheskoi poverkhnosti”, Matem. zametki, 67:2 (2000), 276–287 | MR | Zbl

[3] Briançon J., “Description de $\operatorname{Hilb}^n\mathbb C\{x,y\}$”, Invent. Math., 41 (1977), 45–89 | DOI | MR | Zbl

[4] Mamford D., Lektsii o krivykh na algebraicheskoi poverkhnosti, Mir, M., 1968