His interest in a new area of mathematics, namely projective differential geometry, led to his first paper on the topic appearing in 1921 and, in the same year, he obtained a scholarship from the Ministry of Education to go to Italy and study with Fubini in Turin. Cech studied there between 1921 and 1922 and he clearly impressed Fubini who asked him to cooperate with him in joint project to write a monograph on projective differential geometry.
Kanyang interes sa isang bagong lugar ng matematika, namely projective kaugalian geometry, na humantong sa kanyang unang papel sa topic na lumilitaw sa 1921 at, sa parehong taon, siya na nakuha ng isang scholarship mula sa Ministri ng Edukasyon sa Italya at pag-aaral na may Fubini sa Turin. Cech-aral doon sa pagitan ng 1921 at 1922 at malinaw na siya impressed Fubini na nagtanong sa kanya upang tumulong sa kanya sa pinagsamang proyekto upang makapagsulat ng isang monograp sa projective kaugalian geometry.