https://hal.umontpellier.fr/hal-03413176Bolognesi, MicheleMicheleBolognesiIMAG - Institut Montpelliérain Alexander Grothendieck - UM - Université de Montpellier - CNRS - Centre National de la Recherche ScientifiqueAwada, HanineHanineAwadaStagliano', GiovanniGiovanniStagliano'Some Moduli of $n$-pointed Fano FourfoldsHAL CCSD2021[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Bolognesi, Michele2021-11-03 15:59:172022-08-05 10:51:482021-11-03 15:59:17enPreprints, Working Papers, ...1The object of this note is the moduli spaces of cubic fourfolds (resp., Gushel-Mukai fourfolds) which contain some special rational surfaces. Under some hypotheses on the families of such surfaces, we develop a general method to show the unirationality of the moduli spaces of the $n$-pointed such fourfolds. We apply this to some codimension 1 loci of cubic fourfolds (resp., Gushel-Mukai fourfolds) appeared in the literature recently.