The peritoneum folds back on itself to form the falciform ligament and the right and left triangular ligaments.
From the en.wikipedia.org
An exception to this is the falciform ligament, which attaches the liver to the posterior portion of the anterior body wall.
From the en.wikipedia.org
The umbilical vein enters the abdomen at the umbilicus, and passes upward along the free margin of the falciform ligament of the liver to the inferior surface of the liver.