Timeline for Local deformations of Lagrangian submanifolds in holomorphic symplectic manifold and their intersections

6 events

when toggle format	what		by	license	comment
Mar 22, 2016 at 10:27	history	edited	Lya	CC BY-SA 3.0	added 4 characters in body
Mar 22, 2016 at 9:00	answer	added	abx		timeline score: 2
Mar 22, 2016 at 0:56	comment	added	Tony Pantev		Still, I am not sure why it is expected that the first order deformation determines the intersections. What if we take a linear pencil of high genus curves in a K3, and then take a curve $\Lambda$ in the parameter space of the linear system which is tangent to the line parameterizing the pencil at some point $p$. Then the divisors corresponding to points $t \in \Lambda$ near $p$ will intersect the divisor corresponding to $p$ at a locus that varies with $t$ and has nothing to do with the pencil.
Mar 22, 2016 at 0:25	comment	added	Jason Starr		@TonyPantev. Since the OP asserts that there is a local moduli space, I suspect that $Y$ is intended to be compact, and $X$ is assumed to be smooth and separated at every point of $Y$.
Mar 22, 2016 at 0:13	comment	added	Tony Pantev		Do you have some hidden compactness assumption here? What if you take $X$ to be the cotangent bundle of the complex line (with coordinate $x$), $Y$ to be the zero section and and $Y_{\gamma(t)}$ to be the graph of the closed one form $t(x-t)dx$. In this case the section $s$ is $xdx$ so it vanishes at $x=0$. But $Y_{\gamma(t)}$ intersects $Y$ at the point $x =t$.
Mar 21, 2016 at 22:40	history	asked	Lya	CC BY-SA 3.0