SYZ for index 1 Fano hypersurfaces in projective space

Abstract

We study homological mirror symmetry of the singular hypersurface $X_0=V(t^{n+1}-x_0\cdots x_n)\subseteq {\mathbb{P}}^{n+1}$. Following an SYZ type approach, we produce an LG-model, whose Fukaya-Seidel category recovers line bundles on $X_0$. As a byproduct of our approach, we answer a conjecture of N.Sheridan about generating the small component of the Fukaya category of the smooth index 1 Fano hypersurface in ${\mathbb{P}}^{n+1}$, without bounding co-chains.

50 pages

References in corpus (4)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Landau-Ginzburg models -- old and new
• Lagrangian Floer theory on compact toric manifolds: survey
• Speculations on homological mirror symmetry for hypersurfaces in $({\mathbb{C}}^{\ast }{)}^n$