Thanks to you all. I will take note of all this for the future.

I have tried all that before posting here. I tried reducing by hand all the triangles to quads, and small quads to big quads, and that's not the problem.

I had a bigger problem with another application that I was using before this, and now it seems that there is something in the output that is not good for Poser. I also tested different lights and the problem persists.

Intersecting meshes are not the problem, because if I eliminate them completely and export my object, the problem persists.

I have several modelers, some of them expensive but they produce enormous meshes that are hard to optimize to reach the 45,000 limit polygon that many marketplaces have. That's why I was using a low-poly modeler like Anim8or, but it is not a modeler done with Poser in  mind.

I have purchased Hexagon that seems to not produce meshes with these problems, and has lots of modeling features that I appreciate, and will use in the future.

I will report if I see improvements when I remodel the plane.

Thanks a lot again for your time!