Calabi--Yau 3-folds

This section describes intrinsics that construct Calabi--Yau 3-folds. It also describes a few intrinsics that can be used to study them, but see Section Generic Polarised Varieties for the general intrinsics that apply to all polarised varieties.

The calculations are based on Buckley's Riemann--Roch formula [Buc03] for polarised Calabi--Yau 3-folds with canonical singularities.

CalabiYau(p1,p2,B) : RngIntElt,RngIntElt,GRBskt -> GRCY

The Calabi--Yau 3-fold X, A with h^0(X, A)=p_1, h^0(X, 2A)=p_2 and basket of singularities B.

FindN(X) : GRCY -> RngIntElt,RngIntElt

The first nonnegative value, for the Calabi--Yau 3-fold X, of N_(C_i) (where C_i is the ith curve of the basket of X) together with the distance between successive values of N_(C_i). (The pair 0, 0 is returned if no solutions below the parameter `MaximumN' are found).

FindN(p1,p2,B) : RngIntElt,RngIntElt,GRBskt -> RngIntElt,RngIntElt

The first nonnegative value of N_(C_i) (where C_i is the ith curve of the basket B of 3-fold points and curves and p_1, p_2 are the first two genera) together with the distance between successive values of N_(C_i). (The pair 0, 0 is returned if no solutions below the parameter `MaximumN' are found).