Skip to main content
corrected tex
Source Link

I work on complex numbers. Let $Q \subset \mathbb P^4$ be a quartic threefold that contains a double line $l$. I want to compute the normal sheaf of $l$ in $Q$, and I seem to find only two possible cases, i.e. $$ \mathcal O_l(-1) \oplus \mathcal O_l \text{ and } \mathcal O_l(-2)\oplus \mathcal O_l(1) $$ can

$$\mathcal O_l(-1) \oplus \mathcal O_l\quad\text{and}\quad\mathcal O_l(-2)\oplus \mathcal O_l(1).$$

Can someone tell me which is the right one? There should be some paper by Iskovskikh about that but I am not able to find a copy of that.

I work on complex numbers. Let $Q \subset \mathbb P^4$ be a quartic threefold that contains a double line $l$. I want to compute the normal sheaf of $l$ in $Q$, and I seem to find only two possible cases, i.e. $$ \mathcal O_l(-1) \oplus \mathcal O_l \text{ and } \mathcal O_l(-2)\oplus \mathcal O_l(1) $$ can someone tell me which is the right one? There should be some paper by Iskovskikh about that but I am not able to find a copy of that.

I work on complex numbers. Let $Q \subset \mathbb P^4$ be a quartic threefold that contains a double line $l$. I want to compute the normal sheaf of $l$ in $Q$, and I seem to find only two possible cases,

$$\mathcal O_l(-1) \oplus \mathcal O_l\quad\text{and}\quad\mathcal O_l(-2)\oplus \mathcal O_l(1).$$

Can someone tell me which is the right one? There should be some paper by Iskovskikh about that but I am not able to find a copy of that.

I work on complex numbers. Let Q \subset \PP^4$Q \subset \mathbb P^4$ be a quartic threefold that contains a double line l$l$. I want to compute the normal sheaf of l$l$ in Q$Q$, and I seem to find only two possible cases, i.e.

O_l(-1) \oplus O_l and O_l(-2)\oplus O_l(1)

can $$ \mathcal O_l(-1) \oplus \mathcal O_l \text{ and } \mathcal O_l(-2)\oplus \mathcal O_l(1) $$ can someone tell me which is the right one? There should be some paper by Iskovskikh about that but I am not able to find a copy of that.

I work on complex numbers. Let Q \subset \PP^4 be a quartic threefold that contains a double line l. I want to compute the normal sheaf of l in Q, and I seem to find only two possible cases, i.e.

O_l(-1) \oplus O_l and O_l(-2)\oplus O_l(1)

can someone tell me which is the right one? There should be some paper by Iskovskikh about that but I am not able to find a copy of that.

I work on complex numbers. Let $Q \subset \mathbb P^4$ be a quartic threefold that contains a double line $l$. I want to compute the normal sheaf of $l$ in $Q$, and I seem to find only two possible cases, i.e. $$ \mathcal O_l(-1) \oplus \mathcal O_l \text{ and } \mathcal O_l(-2)\oplus \mathcal O_l(1) $$ can someone tell me which is the right one? There should be some paper by Iskovskikh about that but I am not able to find a copy of that.

Source Link
IMeasy
  • 3.8k
  • 22
  • 37

Normal bundle to a double line in quartic threefold

I work on complex numbers. Let Q \subset \PP^4 be a quartic threefold that contains a double line l. I want to compute the normal sheaf of l in Q, and I seem to find only two possible cases, i.e.

O_l(-1) \oplus O_l and O_l(-2)\oplus O_l(1)

can someone tell me which is the right one? There should be some paper by Iskovskikh about that but I am not able to find a copy of that.