Related papers: Futaki Invariants and Reflexive Polygons
We state Asymptotic Expansion and Growth Rate conjectures for the Witten-Reshetikhin-Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order…
We study the scalar curvature of K\"ahler metrics that have cone singularities along a divisor, with a particular focus on certain specific classes of such metrics that enjoy some curvature estimates. Our main result is that, on the…
We present a general scheme for identifying fibrations in the framework of toric geometry and provide a large list of weights for Calabi--Yau 4-folds. We find 914,164 weights with degree $d\le150$ whose maximal Newton polyhedra are…
We construct a surprisingly large class of new Calabi-Yau 3-folds $X$ with small Picard numbers and propose a construction of their mirrors $X^*$ using smoothings of toric hypersurfaces with conifold singularities. These new examples are…
In the space of couplings of the 4D N=1 gauge theory associated to D3 branes probing Calabi-Yau singularities, there is a manifold over which superconformal invariance is preserved. The AdS/CFT correspondence is valid precisely for this…
We formulate the Asymptotic Expansion Conjecture for the Witten-Reshetikhin-Turaev quantum invariants of closed oriented three manifolds. For finite order mapping tori, we study these quantum invariants via the geometric gauge theory…
We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT,…
This monograph offers an overview on the topological invariants in fermionic topological insulators from the complex classes. Tools from K-theory and non-commutative geometry are used to define bulk and boundary invariants, to establish the…
In this work, we present a new geometric transition in non-compact Calabi-Yau 4-folds, specifically for the cone over the 7d Sasaki-Einstein manifold $Q^{\scriptscriptstyle(1,1,1)}/\mathbb{Z}_{N}$. We discover a new smoothing of such…
We modify the standard perfect symmetric obstruction theory for moduli spaces of simple perfect complexes, to the situation of complexes on abelian threefolds with fixed determinant and Fourier-Mukai determinant. As outcome we attach…
The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge…
In this paper we compute the Futaki invariant of adiabatic Kaehler classes on resolutions of Kaehler orbifolds with isolated singularities. Combined with previous existence results of extremal metrics by Arezzo-Lena-Mazzieri, this gives a…
We carry out a systematic study of a class of 6D F-theory models and associated Calabi-Yau threefolds that are constructed using base surfaces with a generalization of toric structure. In particular, we determine all smooth surfaces with a…
We settle the problem of K-stability of quasi-smooth Fano 3-fold hypersurfaces with Fano index 1 by providing lower bounds for their delta invariants. We use the method introduced by Abban and Zhuang for computing lower bounds of delta…
This paper studies the action of the Fourier-Mukai transform on moduli spaces of vertical torsion sheaves on elliptic Calabi-Yau threefolds in Weierstrass form. Moduli stacks of semistable one dimensional sheaves on such threefolds are…
We calculate the D-brane superpotentials for two Calabi-Yau manifolds with three deformations by the generalized hypergeometric GKZ systems, which give rise to the flux superpotentials $\mathcal{W}_{GVW}$ of the dual F-theory…
Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and ${\cal M}_{\xi}$ a smooth moduli space of fixed determinant semistable vector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smooth anticanonical…
We provide new examples of anti-symplectic involutions on moduli spaces of stable sheaves on K3 surfaces. These involutions are constructed through (anti) autoequivalences of the bounded derived category of coherent sheaves on K3 surfaces…
We develop some ideas of Morrison and Plesser and formulate a precise mathematical conjecture which has close relations to toric mirror symmetry. Our conjecture, we call it Toric Residue Mirror Conjecture, claims that the generating…
Allcock and Freitag recently showed that the moduli space of marked cubic surfaces is a subvariety of a nine dimensional projective space which is defined by cubic equations. They used the theory of automorphic forms on ball quotients to…