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# FUTUR. Portal de la Producció Científica dels Investigadors de la UPC

## Punctured combinatorial Nullstellensätze

Autor
Ball, S.; Serra, O.
Tipus d'activitat
Article en revista
Revista
Combinatorica
Data de publicació
2009
Volum
29
Pàgina inicial
511
Pàgina final
522
DOI
https://doi.org/10.1007/s00493-009-2509-z
URL
http://upcommons.upc.edu/e-prints/handle/2117/1404
Resum
In this article we present a punctured version of Alon's Nullstellensatz which states that if $f$ vanishes at nearly all, but not all, of the common zeros of some polynomials $g_1(X_1),\ldots,g_n(X_n)$ then every $I$-residue of $f$, where the ideal $I=\langle g_1,\ldots,g_n\rangle$, has a large degree. Furthermore, we extend Alon's Nullstellensatz to functions which have multiple zeros at the common zeros of $g_1,g_2,\ldots,g_n$ and prove a punctured version of this generalised version. Some a...
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics