Yes it seems that the marriage record you have is written in Slovak but some of the words that you wrote do not make sense.
Meno rodica a stav : name of the parents and position Irena Bajcar (daughter of) Tomas and Zuzana Cvartner(ova). The ending OVA justs specifies that it is a female, nothing more.
The SK's phone site is at :
www.zoznamst.sk but no surname Cvartner or Crantner. There is a surname BALCAR and in a town of Modra's phone book.
There is a town named Modra in Slovak Republic.
There were 19 SVANTNERs that passed thru Ellis Island and this surname does show up in SK's phone book. Is it possible for me to see this document?