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Naga Venkata
Naga Venkata
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GivenDoes every irreducible component of a Hilbert scheme of curves in $\mathbb{P}^3$ contain a curve that is a union of lines (not necessarily reduced)? Furthermore, given a curve $C \subset \mathbb{P}^3$ does there exists an IRREDUCIBLE family of curves in $\mathbb{P}^3$ such that $C$ is a general fiber and there exists a fiber which is the union of lines (not necessarily reduced)? In other words does every irreducible component of a Hilbert scheme of curves in $\mathbb{P}^3$ contain a curve that is a union of lines (not necessarily reduced)?

Given a curve $C \subset \mathbb{P}^3$ does there exists an IRREDUCIBLE family of curves in $\mathbb{P}^3$ such that $C$ is a general fiber and there exists a fiber which is the union of lines (not necessarily reduced)? In other words does every irreducible component of a Hilbert scheme of curves in $\mathbb{P}^3$ contain a curve that is a union of lines (not necessarily reduced)?

Does every irreducible component of a Hilbert scheme of curves in $\mathbb{P}^3$ contain a curve that is a union of lines (not necessarily reduced)? Furthermore, given a curve $C \subset \mathbb{P}^3$ does there exists an IRREDUCIBLE family of curves in $\mathbb{P}^3$ such that $C$ is a general fiber and there exists a fiber which is the union of lines (not necessarily reduced)?

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Naga Venkata
Naga Venkata
  • 1k
  • 7
  • 14

Deformation of space curves to union of lines

Given a curve $C \subset \mathbb{P}^3$ does there exists an IRREDUCIBLE family of curves in $\mathbb{P}^3$ such that $C$ is a general fiber and there exists a fiber which is the union of lines (not necessarily reduced)? In other words does every irreducible component of a Hilbert scheme of curves in $\mathbb{P}^3$ contain a curve that is a union of lines (not necessarily reduced)?