Geodesic
The number of solutions to some systems of equations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2010), pp. 47-50 
A. N. Zaitseva. The number of solutions to some systems of equations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2010), pp. 47-50. http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a9/
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     author = {A. N. Zaitseva},
     title = {The number of solutions to some systems of equations},
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     pages = {47--50},
     year = {2010},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_2_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

An estimnate for the number of solutions to multi-homogenious systems of equations is obtained using properties of the Hilbert function of multi-homogeneous ideals.