Johannes Nordström
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Registered User
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Feb 18 |
awarded | ● Yearling |
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Feb 3 |
comment |
about decomposition of three forms From the thesis, I see that one is supposed to make some choices of $v \in \Lambda^6 V^*$ and $\theta \in V^*$. $i_X v$ and $\psi \wedge \phi$ are both in $\ker\; i_X \cong \Lambda^5 W^* \subset \Lambda^5 V^*$, so must be proportional. $\ker \theta \to \Lambda^4 W^*, \; Y \mapsto i_Y v_0$ is an isomorphism. |
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Jan 6 |
comment |
Lines on degree 2n-3 Fermat hypersufaces I don't have any references for the specifics of my answer, but I've found the first of Reid's Chapters on Algebraic Surfaces (arxiv.org/abs/alg-geom/9602006) a useful general reference for cubic surfaces. |
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Jan 6 |
accepted | Lines on degree 2n-3 Fermat hypersufaces |
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Jan 5 |
awarded | ● Critic |
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Jan 4 |
comment |
Lines on degree 2n-3 Fermat hypersufaces In the same order as your questions: Yes, I do. If $x$ lies on a line, then that line is contained in $T_xC$, and its defining equation is a factor in $X_0^3 + F$. $F(Y,Z)$ is indeed intended to mean an arbitrary cubic on the line $T_x(C \cap H_0)$; what I try to emphasise (perhaps unsuccessfully) is that the restriction of equation of $C$ to $T_xC \cong \mathbb{P}^2$, which is a cubic in $X_0$, $Y$ and $Z$, does not contain any cross-terms like $X_0Y^2$. |
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Jan 4 |
revised |
A lost lemma about periodicity in a grid of long exact sequences? Update clarifying the question |
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Jan 4 |
revised |
Lines on degree 2n-3 Fermat hypersufaces Corrected Hessian coefficient |
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Jan 4 |
answered | Lines on degree 2n-3 Fermat hypersufaces |
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Jan 3 |
comment |
A lost lemma about periodicity in a grid of long exact sequences? Thanks. The claim in the example from your paper looks slightly different to me, but this kind of reference is helpful. |
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Jan 3 |
revised |
A lost lemma about periodicity in a grid of long exact sequences? Corrected subscripts in statement of lemma |
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Jan 3 |
awarded | ● Student |
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Jan 3 |
asked | A lost lemma about periodicity in a grid of long exact sequences? |
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Jan 2 |
accepted | Almost parallelizable 4-manifolds |
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Jan 1 |
answered | Almost parallelizable 4-manifolds |
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Dec 30 |
comment |
Isometry of K3 surface. Sure, that tells you that for any automorphism of $S$ (of finite order at least) there exists some invariant Kähler class, and hence an invariant Ricci-flat Kähler metric. But it does not mean that a given Ricci-flat Kähler metric is invariant, which is what your question seems to ask. |
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Dec 30 |
answered | Isometry of K3 surface. |
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Dec 30 |
comment |
Isometry of K3 surface. I don't understand the question. Are you implicitly assuming that $g$ is invariant under $\iota$? Why would the choice of complex structure affect whether a map is an isometry? |
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Dec 25 |
comment |
Transforming the Dirac Operator on $S^1$ Could you explain what trivialisation you use when obtaining the local expression $f_1 \rightarrow i\frac{df_1}{dx}$ for the Dirac operator? The transition function $f_1(\frac{1}{x}) = f_2(x)$ suggests the trivialising sections of the spinor bundle is intended to have constant norm. But then the local expression looks to me like the Dirac operator of the Euclidean metric on $\mathbb{R}$, rather than with respect to the metric pulled back from the circle by stereographic projection. |
