Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces

  title={Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces},
  author={H. Nuer},
  journal={arXiv: Algebraic Geometry},
  • H. Nuer
  • Published 2015
  • Mathematics
  • arXiv: Algebraic Geometry
  • We provide explicit descriptions of the generic members of Hassett's divisors $\mathcal C_d$ for relevant $18\leq d\leq 38$ and for $d=44$. In doing so, we prove that $\mathcal C_d$ is unirational for $18\leq d\leq 38,d=44$. As a corollary, we prove that the moduli space $\mathcal N_{d}$ of polarized K3 surfaces of degree $d$ is unirational for $d=14,26,38$. The case $d=26$ is entirely new, while the other two cases have been previously proven by Mukai. 
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