Also, an X volts RMS AC line is 2.8X volts peak-to-peak. The peak voltage is limiting with regards to breakdown voltages, and so DC can reach a higher equivalent voltage on a line with the same maximum voltage.
(The magic component is the "insulated gate bipolar transistor", sometimes using silicon carbide as the semiconducting element. These are capable of multi-kilovolt switching.)
The basic idea is you go to high voltage DC at the generation end, run a long ways (across states), turn the DC to AC and then run that through a transformer. It isn't as efficient as a transformer, but it isn't far behind so you more than get it back by the smaller losses in transmission.
If you consider a voltage source of 1V, a line of 1ohm, with a load of 1ohm (0.25W), the transmission is 50% efficient. With a load of 0.5ohm (0.33W) the line is 33% efficient. with a load of 0ohm it is 0% efficient.
> Also with very high voltage AC we can actually transmit quite far.
We can't transmit efficiently at a quarter the circumference of the globe, which would be required for a continually directly solar powered grid.