Skip to main content
MathOverflow

Return to Answer

added 7 characters in body
Source Link
Charles Siegel
Charles Siegel
  • 16k
  • 8
  • 89
  • 134

There is a map $d\log:H^1(X,\mathcal{O}_X)\to H^1(X,\Omega_X^1)$$d\log:H^1(X,\mathcal{O}_X^\times)\to H^1(X,\Omega_X^1)$ taking a line bundle to it's Chern class (at least, when everything is over $\mathbb{C}$, I believe this works). An ample class is then the Chern class of an ample line bundle.

There is a map $d\log:H^1(X,\mathcal{O}_X)\to H^1(X,\Omega_X^1)$ taking a line bundle to it's Chern class (at least, when everything is over $\mathbb{C}$, I believe this works). An ample class is then the Chern class of an ample line bundle.

There is a map $d\log:H^1(X,\mathcal{O}_X^\times)\to H^1(X,\Omega_X^1)$ taking a line bundle to it's Chern class (at least, when everything is over $\mathbb{C}$, I believe this works). An ample class is then the Chern class of an ample line bundle.

Source Link
Charles Siegel
Charles Siegel
  • 16k
  • 8
  • 89
  • 134

There is a map $d\log:H^1(X,\mathcal{O}_X)\to H^1(X,\Omega_X^1)$ taking a line bundle to it's Chern class (at least, when everything is over $\mathbb{C}$, I believe this works). An ample class is then the Chern class of an ample line bundle.