论文标题
矢量束模量空间的图形电势和符号几何形状
Graph potentials and symplectic geometry of moduli spaces of vector bundles
论文作者
论文摘要
我们给出了具有多个最佳托里的Fano流形的第一个示例，即〜我们构建单调Lagrangian tori $ l $，使得加权的Holomorphic Maslov Index Index index index discs在$ l $上等同于符号的上限，由符号的novectic novectic Invariant $ \ limsup_n（limsup_n（limsup_n（limsup_n）（limsup_n（limsup_n）（limsup_n} n} $ n} $ n]其中$ m_0（l）$是浮动的潜力。 对于每一个三价图$γ$ g $ g $ g $ g $ g $我们将最佳的圆环$l_γ$与著名的Symbletic Fano歧管$ \ Mathcal {n} _g $（复杂尺寸$ 3G-3 $）的$ \ \ \ \ Mathrm {t} _ {属$ g $表面带有规定的奇数单形成术，并在穿刺时，我们还表明所有对$（\ nathcal {n} _g，l_γ）$都是成对的非同位素。特别是，我们确认了对$（\ Mathcal {n} _g，l_γ）$之间的一种镜像对称形式（以及Spaces $ \ Mathcal {n} _g $ standal）和b-Model的图形电位，我们在早期的工作中引入了一家laurent polynomials家族。 A crucial input from outside of symplectic geometry is an analysis of Manon's toric degenerations of algebro-geometric models $\mathrm{M}_C(2,\mathcal{L})$ for the spaces $\mathcal{N}_g$, as moduli spaces of stable rank $2$ bundles on an algebraic curve with a fixed确定性，使用保形场理论构建。
We give the first examples of Fano manifolds with multiple optimal tori, i.e.~we construct monotone Lagrangian tori $L$, such that the weighted number of holomorphic Maslov index two discs with boundary on $L$ equals the upper bound given by the symplectic invariant $\limsup_n ([m_0(L)^n]_{x^0})^{1/n}$, where $m_0(L)$ is the Floer potential. To every trivalent graph $γ$ of genus $g$ we associate an optimal torus $L_γ$ on the celebrated symplectic Fano manifold $\mathcal{N}_g$ (of complex dimension $3g-3$) with $\mathrm{T}_{\mathcal{N}_g} = 8g-8$), given by the character variety of rank 2 on a genus $g$ surface with prescribed odd monodromy at a puncture, We moreover show that all pairs $(\mathcal{N}_g,L_γ)$ are pairwise non-isotopic. In particular, we confirm a form of mirror symmetry between the A-model of the pairs $(\mathcal{N}_g,L_γ)$ (and also spaces $\mathcal{N}_g$ standalone) and B-model of graph potentials, a family of Laurent polynomials we introduced in earlier work. A crucial input from outside of symplectic geometry is an analysis of Manon's toric degenerations of algebro-geometric models $\mathrm{M}_C(2,\mathcal{L})$ for the spaces $\mathcal{N}_g$, as moduli spaces of stable rank $2$ bundles on an algebraic curve with a fixed determinant, constructed using conformal field theory.
