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May
3
reviewed Approve Can the work of Hardy & Ramanujan about partitions shed light on Hardy-Littlewood's k-tuple conjecture?
Apr
29
reviewed Approve Shortest path in a weighted graph with coloured edges
Apr
7
comment Total space of the line bundle $\mathcal{O}(1)$ over $\mathbb{P}^n$
$Tot(\mathcal{O}_{\mathbb{P}^{n}}(k))$ is $\mathbb{P}^{n+1}(1,1,\ldots,1,k) - \{x\}$, where $x = (0:0:\ldots:0:1)$.
Mar
22
comment Local deformations of Lagrangian submanifolds in holomorphic symplectic manifold and their intersections
Nice example with the Fano variety of lines! I still don't understand why you say that the answer of the second question is 'yes'? Your example shows that the answer to the second question is 'no'. and I think my elementary example with a non-linear family of curves on a K3 (in the comment above) also shows that the answer is 'no'. The first one has a chance of being true though.
Mar
22
comment Local deformations of Lagrangian submanifolds in holomorphic symplectic manifold and their intersections
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
comment Local deformations of Lagrangian submanifolds in holomorphic symplectic manifold and their intersections
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
5
reviewed Edit Finite, abelian, yet “fugitive” orthogonal subgroups
Mar
5
revised Finite, abelian, yet “fugitive” orthogonal subgroups
fixed LaTeX typo that was preventing the definition of $\chi_g$ from parsing.
Feb
20
reviewed Approve What's the relationship between the roots of a function and that of a filtered Fourier series representation?
Jan
13
answered Looking for a good exposition - Rees Construction
Nov
13
reviewed Approve Irrationality of $ \pi e, \pi^{\pi}$ and $e^{\pi^2}$
Nov
12
reviewed Approve Compactness of cadlag martingales w.r.t. to the point-wise topology
Oct
16
awarded  Yearling
Jun
25
awarded  Enlightened
Jun
25
awarded  Nice Answer
Mar
27
awarded  Custodian
Mar
27
reviewed Approve One question about iteration on groups
Mar
6
awarded  Enlightened
Mar
6
awarded  Nice Answer
Feb
20
comment Can Enriques Surfaces have non-trivial TWISTED Fourier-Mukai partners?
My guess is that it will be impossible to do it with a genuine surface. One might be able to check this directly by looking at the classification of surfaces, listing all possible twisted Hodge structures, and then checking that the required lattice $E_{8}(-2)\oplus H(2)\oplus H$ can never appear in a twist of a surface. I have not done this carefully but it seems doable. You basically have to rule out K#s and rational elliptic surfaces.