A RIGID CALABI–YAU 3-FOLD

Sara Angela Filippini (1) , Alice Garbagnati

1 I2M - Institut de Mathématiques de Marseille

The aim of this paper is to analyze some geometric properties of the rigid Calabi–Yau threefold Z obtained by a quotient of E 3 , where E is a specific elliptic curve. We describe the cohomology of Z and give a simple formula for the trilinear form on P ic(Z). We describe some projective models of Z and relate these to its generalized mirror. A smoothing of a singular model is a Calabi–Yau threefold with small Hodge numbers which was not known before.

Domaines: Géométrie algébrique [math.AG]

Sara Angela Filippini, Alice Garbagnati. A RIGID CALABI–YAU 3-FOLD. Advances in Theoretical and Mathematical Physics, 2011, 15 (6), pp.1745-1787. ⟨10.4310/ATMP.2011.v15.n6.a4⟩. ⟨hal-01432035⟩