74 lines
2.1 KiB
Markdown
74 lines
2.1 KiB
Markdown
# Calabi-Yau-Period-Geometry
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This project collects code used for analysing Calabi–Yau families.
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It allows for computation of discriminant loci and topological data of manifolds defined as hypersurfaces or complete intersections in toric ambient spaces.
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## toric_topdata
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Supported initialisations are represented by the following examples.
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```python
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elliptic_curve_D = ToricPolytopeProjectiveSpace([1, 2, 3], model_name="elliptic_curve_D")
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CY3_quintic = ToricPolytopeProjectiveSpace([1, 1, 1, 1, 1], model_name="quintic")
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CY3_bicubic = ToricPolytopeCICY([[3, 3]], model_name="bi-cubic")
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CICY3_two_parameter_manual_nef = ToricPolytope([[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],
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[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],
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[-1,-1,0,0,0,0],[0,0,-1,-1,-1,-1]],
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nef_partition=[[0,1,2,3], [4,5,6,7]])
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CICY5_two_parameter = ToricPolytopeCICY([[6, 1],[0, 2]])
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```
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The discriminant factors and topological data, e.g. for the quintic, can then be computed with the methods below.
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```python
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CY3_quintic.disc()
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CY3_quintic.topdata()
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```
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We list the output of above two lines.
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```term
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INFO:__main__:Discriminant factors: [[z1 + 1/3125, 0]]
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INFO:__main__:
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--- Polytope and GLSM table ------------------
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1|1|1|1|1|| 1
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-1|1|0|0|0|| 0
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-1|0|1|0|0|| 0
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-1|0|0|1|0|| 0
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-1|0|0|0|1|| 0
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--------------
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1,1,1,1,1; -5
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--- L-vectors (GLSM charges) -----------------
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[[1, 1, 1, 1, 1, -5]]
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--- Intersection numbers CY ------------------
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{(0, 0, 0): 5}
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--- Intersection ring ------------------------
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5*t0^3
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--- Intersection ring no multiplicities ------
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5*t0^3
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--- Chern polynomials ------------------------
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[[0], [10*t0^3], [-40*t0^3]]
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--- Integrated Chern classes -----------------
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[[0], [50], [-200]]
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DEBUG:__main__:
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--- Kähler cone generators (ambient space) ---
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['[z4]']
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--- Intersection numbers ambient space -------
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{(0, 0, 0, 0): 1}
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```
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The result is saved in the folder `data/topdata` as a JSON file — giving a model name helps keeping
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track of these outputs.
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Note that for Calabi–Yau dimensions larger than four, the additional |