Timeline for How to construct the mirror partner of a blowup?

9 events

when toggle format	what		by	license	comment
May 18, 2017 at 20:27	vote	accept	Nati
May 17, 2017 at 17:13	answer	added	YHBKJ		timeline score: 5
May 17, 2017 at 12:55	comment	added	Tony Pantev		A silly comment - since $X$ is a symplectic specialization of $Z$, $\check{X}$ should be complex specialization of $\check{Z}$. So you will need to understand how to extract a semi-orthogonal decomposition of the Fukaya-Seidel category from a specialization family. For example, the mirror of a del Pezzo $dP_{n}$ is a rational elliptic surface with an $I_{9-n}$ fiber at infinity. The blow-up of $dP_{n}$ at a point corresponds to morsifying one node of the fiber at infinity, i.e. to a splitting it as $I_{1}+I_{9-(n+1)}$ and morsification gives you a semi-orthogonal decomposition of FS.
May 16, 2017 at 22:00	history	edited	Nati	CC BY-SA 3.0	deleted 111 characters in body
May 16, 2017 at 21:50	history	edited	Nati	CC BY-SA 3.0	deleted 111 characters in body
May 16, 2017 at 21:49	comment	added	user21574		Bertie right. In fact if $\pi: \tilde X\to X$ be birational blow up then $K_{\tilde X}=\pi^*(K_X)+E$, so if $c_1(X)=0$ then $c_1(\tilde X)=E$ which is not CY
May 16, 2017 at 21:45	comment	added	Bertie		A minor comment, but since Kodaira dimension is a birational invariant, your $Z$ will never be either Fano or general type; since the canonical bundle is nontrivial, it will not be CY either.
May 16, 2017 at 21:40	history	edited	Nati	CC BY-SA 3.0	added 138 characters in body
May 16, 2017 at 21:31	history	asked	Nati	CC BY-SA 3.0