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Seminários do IMPA

The Noether–Lefschetz theorem tells us that for $d \ge 4$, a very general smooth, degree surface in $\mathbb{P}^3$ has Picard number $1$. Motivated by this theorem, the Noether–Lefschetz locus is defined as the locus of smooth degree $d$ surfaces with Picard number at least $2$. We see the proof of the classical result by Ciliberto–Harris–Miranda which states that the Noether–Lefschetz locus is dense in the space of all smooth, degree d surfaces in $\mathbb{P}^3$.