That maternal nutrition affects a baby's likelihood of developing allergies is nothing new. If you and your partner have eczema, asthma or hay fever, for example, it is advised that you skip peanuts.

A new study suggests that the type of fats in the pregnant mother's diet may also contribute to her child's risk of developing allergies.

High maternal intake of margarine and vegetable oils during the last 4 wk of pregnancy was positively associated and high maternal fish intake was inversely associated with eczema during the first 2 y in the offspring. High celery and citrus fruit intakes increased the risk of sensitization against food allergens. In turn, sensitization against inhalant allergens was positively related to a high maternal intake of deep-frying vegetable fat, raw sweet pepper , and citrus fruit.

The researchers suggest that the intake of allergenic foods and foods rich in n-6 polyunsaturated fatty acids during pregnancy may increase, and foods rich in n-3 polyunsaturated fatty acids may decrease, the risk of allergic diseases in the offspring.

So again, one by one:

Margarine and vegetable oils: Bad, increases risks of eczema
Fish: good, decreases risks of eczema
Celery and Citrus: Bad, increases risks of food sensitivity
Deep-frying Vegetable Fat, Sweet Raw Pepper, Citrus: Bad, increases risks of allergies to airborne allergens

Most likely, the amount of consumption factors in, too. I haven't read the whole article, though (requires subscription or purchase), to verify what levels of consumption they were looking at.