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Vivek Shende
Vivek Shende
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An Enriques surface (in characteristic zero) is an algebraic surface which is the quotient of a K3 surface by a fixed-point-free involution. Such a surface has a rank 10 lattice of divisors.

(1) What are the ample and effective cones of an Enriques surface?

In particular,

(2) Is it the case that there are ample divisors with arbitrarily large numbers of global sections which do not split nontrivially as the sum of two effective divisors?

Edit: As per Damiano's comment,

(3) Is there any surface for which the answer to (2) is yes?

An Enriques surface (in characteristic zero) is an algebraic surface which is the quotient of a K3 surface by a fixed-point-free involution. Such a surface has a rank 10 lattice of divisors.

What are the ample and effective cones of an Enriques surface?

In particular,

Is it the case that there are ample divisors with arbitrarily large numbers of global sections which do not split nontrivially as the sum of two effective divisors?

An Enriques surface (in characteristic zero) is an algebraic surface which is the quotient of a K3 surface by a fixed-point-free involution. Such a surface has a rank 10 lattice of divisors.

(1) What are the ample and effective cones of an Enriques surface?

In particular,

(2) Is it the case that there are ample divisors with arbitrarily large numbers of global sections which do not split nontrivially as the sum of two effective divisors?

Edit: As per Damiano's comment,

(3) Is there any surface for which the answer to (2) is yes?

Source Link
Vivek Shende
Vivek Shende
  • 8.7k
  • 4
  • 39
  • 67

What is known about the ample and effective cones of an Enriques surface?

An Enriques surface (in characteristic zero) is an algebraic surface which is the quotient of a K3 surface by a fixed-point-free involution. Such a surface has a rank 10 lattice of divisors.

What are the ample and effective cones of an Enriques surface?

In particular,

Is it the case that there are ample divisors with arbitrarily large numbers of global sections which do not split nontrivially as the sum of two effective divisors?