## del Pezzo surfaces

Here are the G-functions ()

and regularized quantum periods ()

for del Pezzo surfaces.

### The del Pezzo surface of degree 9

This is the toric variety . We have:

and the regularized quantum period is:

### The del Pezzo surface of degree 8, case a

This is the toric variety . We have:

and the regularized quantum period is:

### The del Pezzo surface of degree 8, case b

This is the toric variety . We have:

and the regularized quantum period is:

### The del Pezzo surface of degree 7

This is the blow-up of in two points. It is a toric variety. We have:

and the regularized quantum period is:

### The del Pezzo surface of degree 6

This is the blow-up of in three points. It is a toric variety. We have:

and the regularized quantum period is:

### The del Pezzo surface of degree 5

This is a hypersurface of bidegree in . We have:

and the regularized quantum period is:

### The del Pezzo surface of degree 4

This is a (2,2) complete intersection in . We have:

and the regularized quantum period is:

### The del Pezzo surface of degree 3

This is the cubic surface in . We have:

and the regularized quantum period is:

### The del Pezzo surface of degree 2

This is the quartic surface in . We have:

and the regularized quantum period is:

### The del Pezzo surface of degree 1

This is the sextic surface in . We have:

and the regularized quantum period is:

See the previous incarnation of this page:

http://coates.ma.ic.ac.uk/fanosearch/?p=5093

for some informative comments.

The (anticanonical) spectra of del Pezzo surfaces.

(T=3)

(T=4)

(T~3.79)

(T~4.72)

(T=6)

(T~8.09)

(T=12)

(T=21)

(T=52)

(T=372)

Copy-paste edition:

c9 = 1-27*t^3;

cq = t^2*(1-16*t^2);

c8 = 1 + t – 8*t^2 – 36*t^3 – 11*t^4;

c7 = (1+t) * (1 + t – 18*t^2 – 43*t^3);

c6 = (1+3*t)*(1+2*t)*(1-6*t);

c5 = (1+3*t)*(1-5*t-25*t^2);

c4 = (1+4*t)(1-12*t);

c3 = (1+6*t)*(1-21*t);

c2 = (1+12*t)*(1-52*t);

c1 = (1+60*t)*(1-372*t);