Hi,
I'm not following you.
What do you mean by "when i trying to show three or more chracteristic option in product page" ?
I was talking about creating custom fields of the table "product", not characteristics. And you can have as many custom product fields as you want with problem.
Are you talking about a new issue, unrelated your initial request ? In that case, please open a new thread in the future in order to avoid confusion.
When you add characteristics to a product, you need to generat the variants, one for each combination of values of all the characteristics. And above a few hundred variants, even the biggest web servers will have issues displaying the product page because there will be too much data to be loaded on the page (that's why there is a pagination on products listings, so that the web server doesn't have to load the data of all the products at once, and a variant has the same amount of data as a product, so if you have hundreds of variants for a product, it's the same as trying to load a products listing with hundreds of products).
The goal of variants is to be able to manage different stock/price/image for each variant. I suppose you don't need this (at least not for all the characteristics). So it's likely that instead of characteristics, you want to use options or custom fields of the table "item". With options/custom item fields, you can have as much of them as you need, because they don't generate variants.