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+# Twisted Hodge numbers for complete intersections
+
+The file `twisted.sage` implements the computation of twisted Hodge numbers for complete intersections, due to Brückmann in the following papers
+
+* [MR0399102] Brückmann, Peter: Zur Kohomologie von projektiven Hyperflächen.
+  Beiträge zur Algebra und Geometrie, 2. 4 (1973), 87–101 (1974).
+
+* [MR0417202] Brückmann, Peter: Zur Kohomologie von vollständigen Durchschnitten mit Koeffizienten in der Garbe der Keime der Differentialformen.
+  Math. Nachr. 71 (1976), 203–210.
+
+* [MR0447266] Brückmann, Peter: Zur Kohomologie von vollständigen Durchschnitten mit Koeffizienten in der Garbe der Keime der Differentialformen. II.
+  Math. Nachr. 77 (1977), 307–318.
+
+## Getting started
+
+Make sure that Sage knows about `twisted.sage`, probably by doing `load("twisted.sage")`. There is ample documentation in the file, which can be acessed via
+
+```sage
+twisted_hodge_number?
+TwistedHodgeDiamond?
+```
+
+To get the (untwisted) Hodge diamond of a quartic surface, use
+
+```sage
+sage: TwistedHodgeDiamond((3, 4))
+          1
+      0        0
+  1       20       1
+      0        0
+          1
+```
+
+This luckily agrees with the output for
+
+```
+sage: TwistedHodgeDiamond((4, [3, 2]))
+sage: TwistedHodgeDiamond((5, [2, 2, 2]))
+```
+
+If you rather care about *twisted* Hodge diamonds (otherwise you could also use the [Hodge diamond cutter](https://github.com/pbelmans/hodge-diamond-cutter), one can compute it for say projective 3-space, twisted by `O(4)` (so that we are in fact computing the Hochschild-Kostant-Rosenberg decomposition of Hochschild cohomology) as follows
+
+```sage
+sage: TwistedHodgeDiamond((3, []), 4)
+              35
+          0        45
+      0       0         15
+  0       0        0         1
+      0       0         0
+          0        0
+              0
+```
+
+For more information, see the docstrings.
+
+Also check out the documentation for the auxiliary class `CompleteIntersection`, and if you are into Hochschild cohomology the class `PolyvectorParallelogram`.
+
+## Authors
+
+* [**Pieter Belmans**](https://pbelmans.ncag.info)
+* **Piet Glas**
+