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Wayne
Wayne
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Suppose we have a principally polarized abelian variety X over the complex number field. Also suppose given Given two ample, effective divisors D_1, D_2 representing two amplesuch that the global sections of both line bundles inare 1 dimensional vector spaces. If D_1 and D_2 have the same principle polarizationfirst Chern class, then is it true that D_1 and D_2 differ by a translation, i.e., there is x in X such that D_1 + x = D_2 as divisors? Why or why not?

Then is it true that D_1 and D_2 differ by a translation, i.e., there is x in X such that D_1 + x = D_2 as divisors? Why or why not?

Suppose we have a principally polarized abelian variety X over the complex number field. Also suppose given two effective divisors D_1, D_2 representing two ample line bundles in the same principle polarization.

Then is it true that D_1 and D_2 differ by a translation, i.e., there is x in X such that D_1 + x = D_2 as divisors? Why or why not?

Suppose we have a principally polarized abelian variety X over the complex number field. Given two ample, effective divisors D_1, D_2 such that the global sections of both line bundles are 1 dimensional vector spaces. If D_1 and D_2 have the same first Chern class, then is it true that D_1 and D_2 differ by a translation, i.e., there is x in X such that D_1 + x = D_2 as divisors? Why or why not?

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Ben Webster ♦
Ben Webster ♦
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theta divisor on a ppavprincipally polarized abelian variety

Suppose we have a ppavprincipally polarized abelian variety X over the complex number field. Also suppose given two effective divisors D_1, D_2 representing two ample line bundles in the same principle polarization. Then is it true that D_1 and D_2 differ by a translation, i.e., there is x in X such that D_1 + x = D_2 as divisors. Why or why not?

Then is it true that D_1 and D_2 differ by a translation, i.e., there is x in X such that D_1 + x = D_2 as divisors? Why or why not?

theta divisor on a ppav

Suppose we have a ppav X over the complex number field. Also suppose given two effective divisors D_1, D_2 representing two ample line bundles in the same principle polarization. Then is it true that D_1 and D_2 differ by a translation, i.e., there is x in X such that D_1 + x = D_2 as divisors. Why or why not?

theta divisor on a principally polarized abelian variety

Suppose we have a principally polarized abelian variety X over the complex number field. Also suppose given two effective divisors D_1, D_2 representing two ample line bundles in the same principle polarization.

Then is it true that D_1 and D_2 differ by a translation, i.e., there is x in X such that D_1 + x = D_2 as divisors? Why or why not?

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Wayne
Wayne
  • 377
  • 2
  • 10

theta divisor on a ppav

Suppose we have a ppav X over the complex number field. Also suppose given two effective divisors D_1, D_2 representing two ample line bundles in the same principle polarization. Then is it true that D_1 and D_2 differ by a translation, i.e., there is x in X such that D_1 + x = D_2 as divisors. Why or why not?