Super-resolution techniques such as MUSIC can be used for creating higher resolution nulls (see MUSIC-based steering vector used in adaptive nulling suppression for example), but what I think may be missed is how beamforming antenna arrays readily allow for the creation of nulls that are narrower than the antenna beam-width without the use of more advanced "super-resolution" techniques. This is simply a property of the transversal structure in the way the beam is formed; we can readily create sharp nulls but cannot create similarly sharp peaks. With the beamformer structure we have the ability to place zeros (but not poles) in a specific direction, and can group several zeros together.
The beam pattern for an antenna array is the spatial version of what is temporal in an FIR filter, where as an "all-zero" structure we also have the option to concentrate zeros in one spatial direction. This is clearer with understanding the similarities between an FIR filter and a beamformer, and how poles and zeros affect the frequency response in filter design.
An FIR filter is a "transversal in time" structure; while a beamformer is "transversal in space". With the FIR filter we have an output that is the sum of multiple copies of the input each delayed or offset in time and individually scaled. With the antenna array we get the same thing, except offset in time is replaced with offset in space: We have multiple copies of the input signal as received by different antennas at different spatial locations. If each individual antenna was omni-directional and with proper spacing that is synonymous with the unit sample delay in an FIR filter ($z^{-1}$), we can predict and design antenna patterns using FIR design tools! (We still can in other cases, we just need to work in the individual antenna patterns as well).
That said, here is then the straight forward answer to the question. Like the FIR filter, the system is all zeros with only trivial poles at the origin on the z-plane. The antenna pattern is found by sweeping $z$ on the unit circle corresponding to spatial direction according to the antenna spacing. Thus by proper scaling prior to the summing of each element, we can place zeros toward one particular direction to achieve the null in that spatial direction.
Demonstrating this is a 13 element antenna array using firls to concentrate rejection in the broadside angle direction of $0.35\pi$ to $0.40\pi$ as follows:
coeff = sig.firls(13, [0, .2, .35, .4, .5, 1], [1, 1, 0, 0, 1, 1])
The resulting pattern when plotted as we would typically view a filter frequency response (which this is!) is given below:
And when plotted as a typical antenna pattern on a polar plot of magnitude in dB versus angle of arrival it would appear as shown below:
Note that in the plot above 0 to 180 degrees corresponds to the front direction of the antenna and 180 to 360 is the backlobe for a linear antenna array. It is typical to have the front centered on 0 degrees instead of 90 degrees as done above, in which case the above pattern should be rotated clockwise 90 degrees- I left as is to be consistent with the frequency axis returned from the frequency response tools).
When reviewing the roots (zeros) for this derived solution, we see how two of the zeros have been concentrated together on the unit circle in the direction of the null. The solution for the other zeros is such that we get a minimum least squares error from unity gain for all other directions with maximum rejection at the null within the constraint of a linear-phase spatial solution (given what firls provides, not that a linear-phase solution is necessary for this).
