Fano 4-folds having a prime divisor of Picard number 1

Abstract

We give a complete classification of smooth, complex projective Fano 4-folds of Picard number 3 having a prime divisor of Picard number 1. They form 28 distinct families, and we compute the main numerical invariants, study the base locus of the anticanonical divisor, and give a comment on rationality. Furthermore, we give an upper bound of both the dimension of the automorphism group and the dimension of the base of the Kuranishi family of a general member.

v2: 15 pages, minor changes and adjustements after reviewer's suggestions. Corrected Remark 2.3. Added Lemma 3.2 and Lemma 3.5 to make the computations in section 3 clearer. Updated and corrected references

References in corpus (2)

• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
• Remarks on Automorphism and Cohomology of Cyclic Coverings