All Questions
Tagged with complex-geometry reference-request
213
questions
2
votes
0
answers
46
views
Stability on manifold with boundary
Let $(X,\partial X)$ a smooth Kahler manifold with boundary, i.e. the interior of $X$ is Kahler, Donaldson proved that:
Given a smooth vector bundle $E$ over $X$ such that $E$ is holomorphic over the ...
- 345
0
votes
0
answers
108
views
Reference request. Looking for a specific compact complex manifold
For my research I need to construct a compact complex manifold with quartic ramification loci. By quartic ramification loci I mean that $L_1,L_2,L_3$ are complex algebraic varieties of degree four and ...
- 189
2
votes
0
answers
68
views
Existence of meromorphic differential form on curve with given multiplicity of zeroes and poles
Let $m \in \mathbb{Z}^n$ be a partition of $2g-2$. Polishuk showed in his paper "Moduli spaces of curves with effective r-spin structures" (arXiv link) that if all entries of $m$ are ...
- 203
6
votes
0
answers
195
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Reference request: Automorphisms of $\mathbb C\{x,y\}$ which preserve the equation of the cusp, $x^3 - y^2$
In my research I encountered automorphisms of the ring of convergent power series
$$\varphi: \mathbb C\{x,y\} \to \mathbb C\{x,y\},$$
which preserve $f = x^3 - y^2$, i.e. $\varphi(f) = f$. I'm ...
- 1,141
1
vote
0
answers
151
views
Reference for application of local cohomology to complex manifolds with points removed
Reference request - I am looking at Dolbeault cohomology on compact complex manifolds (not Riemann surfaces) with points removed. I have been told that the key to doing this is to look at Local ...
- 1,213
3
votes
1
answer
410
views
Finding global sections of a sheaf of sets using (some kind of) sheaf cohomology?
Let $X$ be a compact manifold, say, and $G$ a Lie group, and $H$ a closed Lie subgroup such that $M \cong G/H$ is a homogeneous space. (For my purposes, $X$ and $M$ would be a smooth projective ...
- 1,755
2
votes
0
answers
86
views
A paper that proves the blowup of the projective plane has positive holomorphic sectional curvature
I'm convinced I've read a paper where the authors prove that the blowup of the projective plane in a single point admits a metric of positive holomorphic sectional curvature. This was not the main ...
- 4,231
4
votes
1
answer
177
views
Effective bound on "Jacobian rank" for (regular) planar algebraic curves
Let an irreducible, square-free complex polynomial $f\in \mathbb C[x,y]$ be given. It is well known that the curve $\mathcal C:=\{f=0\}$ is nonsingular if and only if $\mathbb C[x,y]=<f,\partial_xf,...
- 5,298
3
votes
1
answer
164
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Can we define $\partial\bar{\partial}(\log|z_1|^2)\wedge \partial\bar{\partial}(\log|z_2|^2)$ as a current?
In complex analysis, by Poincare-Lelong theorem, we have
$$
\frac{\sqrt{-1}}{\pi}\partial\bar{\partial}(\log|z|^2)=T_{z=0}
$$
as currents, where
$$
T_{z=0}(\eta)=\int_{z=0}\eta.
$$
Now suppose we have ...
- 8,767
4
votes
0
answers
107
views
Degeneration formula and Donaldson-Floer theory
Is there a relation between the degeneration formula of GW Invariants of Jun Li and the Donaldson-Floer theory? Is there an example / discussion anywhere of/on this relation?
- 153
2
votes
0
answers
107
views
Looking for a proof of a result of Grauert and Kerner
I'm looking for a proof of the following result.
Let $X$ be a Stein manifold and $h: Z \to X$ be a holomorphic fibre bundle with a complex homogeneous fibre whose structure group is a complex Lie ...
- 1,755
5
votes
1
answer
219
views
Does $F_{A}^{0,2}=0$ for a connection $A$ on $TM$ almost complex give a complex structure?
First, some motivation. Let $X$ be a complex manifold, and $A$ a Hermitian connection on some complex vector bundle $E$ over $X$. It is known that the existence of $A$ such that the $(0,2)$-part of ...
- 1,755
2
votes
0
answers
147
views
Steenbrink spectral sequence and modifications of the central fibre
If $f: X \to S$ is a proper map from a complex manifold to a disc, $Y=f^{-1}(0)$ is a divisor with strictly normal crossings and the action of monodromy on $X_t=f^{-1}(t)$ for some (hence any) $t \neq ...
- 4,060
-1
votes
1
answer
92
views
Related to the Schwarz Christoffel map
With the help of the Schwarz-Christoffel map, for a given polygon (given angle), we can find some points on the boundary of the upper half plane, such that a particular Schwarz-Christoffel map takes ...
- 541
2
votes
1
answer
260
views
On the stack of semistable curves
This is a question related to
Semistable curves of genus $g\geq 2$ form an Artin algebraic stack in the etale topology?
Let $\mathcal C\rightarrow \mathcal M^{ss}_g$ be the universal curve over the ...
- 492