%0 Journal Article %T On Minkowski decomposition of Okounkov bodies on a Del Pezzo surface %A Patrycja £¿uszcz-£¿widecka %J Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica %D 2011 %I Krak¨®w : Wydawnictwo Naukowe Uniwersytetu Pedagogicznego %X We show that on a blow up of $P^2$ in $3$ general points there exists a finite set of nef divisors $P_1,ldots,P_s$ such that the Okounkov body $Delta(D)$ of an arbitrary effective $R$--divisor $D$ on $X$ is the Minkowski sum Delta(D)=sum_{i=1}^s a_iDelta(P_i) (1) with non-negative coefficients $a_i in R_{geq 0}$. %U http://studmath.up.krakow.pl/index.php/studmath/article/view/119