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invariants of *smooth* varieties
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The dimensions $h^i(\mathcal O_X)$ of the cohomology groups of $\mathcal O_X$, and thus the Euler characteristic, are birational invariants of smooth proper varieties in positive characteristic as well, by a recent work of Andre Chatzistamatiou and Kay Rülling. It is not published yet but a preprint is available.

The dimensions $h^i(\mathcal O_X)$ of the cohomology groups of $\mathcal O_X$, and thus the Euler characteristic, are birational invariants of proper varieties in positive characteristic as well, by a recent work of Andre Chatzistamatiou and Kay Rülling. It is not published yet but a preprint is available.

The dimensions $h^i(\mathcal O_X)$ of the cohomology groups of $\mathcal O_X$, and thus the Euler characteristic, are birational invariants of smooth proper varieties in positive characteristic as well, by a recent work of Andre Chatzistamatiou and Kay Rülling. It is not published yet but a preprint is available.

Source Link
VA.
VA.
  • 13.1k
  • 2
  • 50
  • 63

The dimensions $h^i(\mathcal O_X)$ of the cohomology groups of $\mathcal O_X$, and thus the Euler characteristic, are birational invariants of proper varieties in positive characteristic as well, by a recent work of Andre Chatzistamatiou and Kay Rülling. It is not published yet but a preprint is available.