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user221330
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I'm attempting to understand the Bombieri-Lang Conjecture:

If $X$ is a smooth projective variety of general type defined over a number field, then the set of rational points of $X$ is not dense.

If $X$ is a smooth projective variety of general type defined over a number field, then the set of rational points of $X$ is not dense.

I don't understand what it means for a variety to be ''of general type''. I know it's when the variety's Kodaira dimension is maximal, but this doesn't mean much to me. Is there an equivalent condition, or more intuitive way to visualise Kodaira dimension?

I'm attempting to understand the Bombieri-Lang Conjecture:

If $X$ is a smooth projective variety of general type defined over a number field, then the set of rational points of $X$ is not dense.

I don't understand what it means for a variety to be ''of general type''. I know it's when the variety's Kodaira dimension is maximal, but this doesn't mean much to me. Is there an equivalent condition, or more intuitive way to visualise Kodaira dimension?

I'm attempting to understand the Bombieri-Lang Conjecture:

If $X$ is a smooth projective variety of general type defined over a number field, then the set of rational points of $X$ is not dense.

I don't understand what it means for a variety to be ''of general type''. I know it's when the variety's Kodaira dimension is maximal, but this doesn't mean much to me. Is there an equivalent condition, or more intuitive way to visualise Kodaira dimension?

Source Link
user221330
user221330
  • 487
  • 3
  • 9

Understanding what it means to be ''of general type''

I'm attempting to understand the Bombieri-Lang Conjecture:

If $X$ is a smooth projective variety of general type defined over a number field, then the set of rational points of $X$ is not dense.

I don't understand what it means for a variety to be ''of general type''. I know it's when the variety's Kodaira dimension is maximal, but this doesn't mean much to me. Is there an equivalent condition, or more intuitive way to visualise Kodaira dimension?