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Apr
6
awarded  Enlightened
Apr
6
awarded  Nice Answer
Apr
3
answered On a question motivating Lurie's treatment of formal moduli problems
Dec
4
revised Branch loci of Ramified covers
deleted 6 characters in body
Dec
3
awarded  Nice Answer
Dec
3
revised Branch loci of Ramified covers
added 8 characters in body
Nov
27
revised Branch loci of Ramified covers
edited body
Nov
27
answered Branch loci of Ramified covers
Oct
16
awarded  Yearling
Oct
10
awarded  Constituent
Oct
1
awarded  Caucus
Sep
27
comment Representation variety vs. space of flat connections
The holonomy does not provide such a bijection. It only provides a bijection between the space of flat connections on the trivial bundle and a connected component of of the representation variety. Often the representation variety will have more components. If $M$ is a compact manifold and $G$ is a complex reductive group, then this bijection is a homeomorphism. In fact if $M$ is a complex projective algebraic variety, the bijection is a complex analytic isomorphism.
Sep
13
comment Coherent sheaf with Vanishing chern classes
It doesn't have to be locally free. If $p$ is a point on a smooth curve $C$, then $\mathcal{O}_{C}(-p)\oplus \mathcal{O}_{p}$ has trivial first Chern class.
Aug
9
comment A reference about Dolbeault cohomology
Can you clarify the question? The Dolbeault cohomology is defined with coefficients in any flat unitary holomorphic bundle or more generally with coefficients in any holomorphic Higgs bundle. I don't see what positivity has to do with the definition. Are you thinking about a harmonic metric somehow?
Jun
25
awarded  ag.algebraic-geometry
May
30
comment A question on the topological change of dualizing a SLAG fibration.
The fact that the minimal resolution of the compactified relative Picard is again a K3 can be checked directly from Kodaira's classification of singular fibers. The type of the singular fiber is determined by the local monodromy and the local monodromy doesn't change under dualization because it is in $SL_2$. Once you know that singular fibers are the same as the original ones, the canonical class formula for an elliptic surface tells you that you have a K3. This doesn't work in higher dimensions already topologically as Mark explained above.
May
29
answered A question on the topological change of dualizing a SLAG fibration.
Feb
5
revised Hitchin fibration outside of type A
added 2 characters in body
Feb
5
answered Hitchin fibration outside of type A
Oct
16
awarded  Yearling