Ask Mr. Smarty Plants

What you are probably referring to is allelopathy, which is the production of chemicals in some plants that inhibit growth in competing plants nearby. This article from Cornell University includes this statement:

"One of the most famous allelopathic plants is Black Walnut (Juglans nigra).  The chemical responsible for the toxicity in Black Walnut is Juglone (5 hydroxy-1,4 napthoquinone) and is a respiration inhibitor.  Solanaceous plants, such as tomato, pepper, and eggplant, are especially susceptible to Juglone.  These plants, when exposed to the allelotoxin, exhibit symptoms such as wilting, chlorosis (foliar yellowing), and eventually death.  Other plants may also exhibit varying degrees of susceptibility and some have no noticeable effects at all.  Some plants that have been observed to be tolerant of Juglone include lima bean, beets, carrot, corn, cherry, black raspberry, catalpa, Virginia creeper, violets, and many others."

Black walnut isn't the only tree that produces juglone. This chemical is also secreted in smaller amounts by English walnut, hickory and pecan trees.Other trees with allelopathic properties include tree-of-heaven, sugar maple, hackberry, American sycamore, American elm, southern wax myrtle, cottonwood, black cherry, sassafras, red oak and black locust.

So, we know about Black Walnut not being a threat to your corn, now to find out if Celtis laevigata (Sugar hackberry), which is a member of the Ulmaceae (elm) family, could exibit allelopathy. We found this list of pests in corn:

• Spotted Cucumber Beetles
• Flea Beetles
• Cutworms
• Corn Rootworms
• Raccoons

Frankly, we think any of them would be worse than a nearby hackberry. Since the center of origin of  Zea mays (corn) is believed to be native to Mexico or Central America, we don't know  too much about it. If your (native) hackberry is shading the corn, you might want to think about it, but otherwise, we feel the corn is safe.