Timeline for Veronese surfaces in $\mathbb{P}^5$ intersecting finitely

7 events

when toggle format	what		by	license	comment
Dec 11, 2019 at 18:27	vote	accept	DCT
Dec 11, 2019 at 6:12	comment	added	Sasha		@DCT: You are right again, and I was a bit hasty. What the spectral sequence gives, it is "roughly" an exact sequence $0 \to H^0(X_2,\mathcal{O}_W) \to \mathbb{C}^6 \oplus \mathbb{C}^9 \to H^0(X_2,I_W(4)) \to 0$, so the actual bound is 15. Of course you can improve it a bit since you know that the second map cannot be identically zero. In fact, it is quite possible that you can establish the bound 10 in this way (for this you have to show that $X_1$ cannot be contained in 2 out of 6 quadrics through $X_2$).
Dec 11, 2019 at 3:59	comment	added	DCT		I think I can follow your reasoning to get the last exact sequence, but apparently $W$ could be 10 simple points. Do you know how to resolve the apparent contradiction?
Dec 10, 2019 at 19:45	history	edited	Sasha	CC BY-SA 4.0	added 1886 characters in body
Dec 10, 2019 at 19:28	comment	added	Sasha		@DCT: You are right, one needs a bit more in this case, I will extend the answer.
Dec 10, 2019 at 19:15	comment	added	DCT		In this case, $X_1$ and $X_2$ are dimension 2 in $\mathbb{P}^5$. If they intersect in finitely many points, does this count as dimensionally transverse?
Dec 10, 2019 at 4:23	history	answered	Sasha	CC BY-SA 4.0