On the classficiation of Kähler-Ricci solitons on Gorenstein del Pezzo surfaces
Calculation for the preprint arXiv:1705.02920.
List of Gorenstein del Pezzo surfaces with 1-torus action
Degree 1, Sing=
Degree 2, Sing=
Degree 2, Sing=
Degree 3, Sing=
Degree 3, Sing=
Degree 4, Sing=
Degree 4, Sing=
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.
Step (i) -- obtain a closed form for
For this we have to analytically solve the integral .
Step (ii) -- find an estimate for the soliton candidate vector field
Step (iii) & (iv) -- obtain closed forms for and plug in the estimate for
For every choice of we have to symbolically solve the integrals , which up to scaling with a positive constant coincide with . Then we plug in the estimate for into the resulting expression.