Minimum check in time at Zurich is 2 hours. Provided you checked in on time, they cannot deny boarding to you without compensation. Go to delta.com and search "contract of carriage" in the search box. You will find all the details regarding voluntary and involuntary denied boarding.
From the website:
Amount of Involuntary Denied Boarding CompensationIf all conditions for compensation are met, then Delta shall pay compensation to passengers involuntarily
denied boarding in an amount to be calculated as follows:
1. Where Delta arranges Qualifying Alternative Transportation
If Delta arranges Qualifying Alternative Transporta
tion, then Delta will pay denied boarding compensation in
an amount equal to 200% of the fare (including any surcharges and air transportation taxes) to the
passenger's next stopover, or if none, to
his/her final destination, but not more than USD 650.00. Qualifying
Alternative Transportation means comparable air tran
sportation, or other transportation used by the
passenger, at no extra cost to the passenger, that at t
he time such arrangements are made, is scheduled to
arrive at the passenger's next stopover, or, if none, final
destination within two hours after the planned arrival
time of the passenger's original flight or flights.
2. Where Delta cannot arrange
Qualifying Alternative Transportation
If Delta cannot arrange Qualifying Alternative Tr
ansportation, then Delta will pay denied boarding
compensation in an amount equal to 400% of the fare
(including any surcharges and air transportation taxes)
to the passenger's next stopover, or if none, to his/
her final destination, but not more than USD 1300.00.
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