  Star configurations of points are configurations with known (and conjectured)
extremal behaviors among all configurations of points in $\mathbb P_k^n$;
additional interest come from their rich structure, which allows them to be
studied using tools from algebraic geometry, combinatorics, commutative algebra
and representation theory. In the present paper we investigate the more general
problem of determining the structure of symbolic powers of a wide
generalization of star configurations of points (introduced by Geramita,
Harbourne, Migliore and Nagel) called star configurations of hypersurfaces in
$\mathbb P_k^n$. Here (1) we provide explicit minimal generating sets of the
symbolic powers $I^{(m)}$ of these ideals $I$, (2) we introduce a notion of
$\delta$-c.i. quotients, which generalize ideals with linear quotients, and
show that $I^{(m)}$ have $\delta$-c.i. quotients, (3) we show that the shape of
the Betti tables of these symbolic powers is determined by certain "Koszul"
strands and we prove that a little bit more than the bottom half of the Betti
table has a regular, almost hypnotic, pattern, and (4) we provide a closed
formula for all the graded Betti numbers in these strands. As a special case of
(2) we deduce that symbolic powers of ideals of star configurations of points
have linear quotients. We also improve and extend results by Galetto, Geramita,
Shin and Van Tuyl, and provide explicit new general formulas for the minimal
number of generators and the symbolic defects of star configurations. Finally,
inspired by Young tableaux, we introduce a technical tool which may be of
independent interest: it is a "canonical" way of writing any monomial in any
given set of polynomials. Our methods are characteristic--free.
