1 3 M ay 2 01 0 The curve of lines on a prime Fano threefold of genus 8

  • F. FLAMINI-E. SERNESI
A complex projective three-dimensional nonsingular variety X is a prime Fano threefold if it has second Betti number B 2 = 1 and Pic(X) is generated by −K X. The (even) integer (−K X) 3 is called the degree of X and g := 1 2 (−K X) 3 + 1 ≥ 2 is the genus of X. It is well known that prime Fano threefolds of genus g exist only for 2 ≤ g ≤ 10 or g = 12. Some… CONTINUE READING