Let $\mathcal O_{2A_1}$ be the next-to-minimal nilpotent orbit of the complex simple Lie algebra of type $E_7$. Let $\mathfrak p_7$ be the maximal parabolic subalgebra corresponding to the simple root $\alpha_7$, and let $\mathfrak u^+$ be its nilpotent radical. We prove that the affinization $T^*(\mathcal O_{2A_1}\cap\mathfrak u^+)^{\mathrm{aff}}$ of the cotangent bundle of $\mathcal O_{2A_1}\cap\mathfrak u^+$ is isomorphic to the nilpotent orbit closure $\overline{\mathcal O}_{2A_1}$ as affine varieties.
Let $f$ be a regular endomorphism of $\mathbb{A}_{\mathbb{C}}^N$ and let $C\subseteq\mathbb{A}_{\mathbb{C}}^N$ be an irreducible curve. Suppose $C$ has an infinite intersection with the $f$-orbit of a point $x\in\mathbb{A}^N(\mathbb{C})$. Then the normalization of $C$ is isomorphic to either $\mathbb{A}^1$ or $\mathbb{...
By studying wall crossings of Hassett moduli spaces of weighted pointed curves, we prove a recursive formula that reduces the computation of the cohomology of $\overline{\mathcal M}_{g,n}$ to that of the moduli space $\overline{\mathcal M}_{g,(0^+)^n}$ of stable pointed curves of minimal weights. For $g=1$, we further...
Let $\mathcal O$ be a nonzero nilpotent orbit in a complex simple Lie algebra $\mathfrak g$. For $\mathfrak g$ of classical type, we classify the orbit closures $\overline{\mathcal O}$ that are isomorphic to $(T^*X)^{\mathrm{aff}}$ for a smooth quasi-affine variety $X$. In types $G_2$, $F_4$, and $E_8$, we show that no...
Let $\Sigma$ be a closed oriented surface of genus $>1$ and $M$ a complete hyperbolic 3-manifold with a marking $i:\Sigma\longrightarrow M$. We consider the case that $M$ has no parabolic cusps and at least one of the two ends is simply degenerate. For $\varGamma=\pi_1(\Sigma)$, let $\rho_M:\varGamma\longrightarrow \ma...
Let $(V_i,\omega_i)$ be real symplectic vector spaces and let $\Omega_i\in\mathcal U^+(V_i)$ in the sense of Haiden. We prove that $p_1^*\Omega_1\wedge p_2^*\Omega_2$ belongs to $\mathcal U^+(V_1\oplus V_2)$ whenever one factor has real dimension at most six. There are forms $\Omega\in\mathcal{U}^+(\mathbb{R}^6)\setmin...
Let $\Omega$ be the Lorentz future cone in $\mathbb{R}^{d+1}$ with respect to the Lorentz product and let $T^M$ be the $M$-fold product of the future tube $T=\mathbb{R}^{d+1}+i\Omega$. The Lorentz group $\mathrm{SO}_0(1,d)$ acts diagonally on $T^M$, and its complexification $\mathrm{SO}(1,d)^\mathbb{C}$ acts on $\mathb...
Maxim Kukol· 0 citations
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