Related papers: The Calabi-Yau conjectures for embedded surfaces

A "folklore conjecture, probably due to Tutte" (as described in [P.D. Seymour, Sums of circuits, Graph theory and related topics (Proc. Conf., Univ. Waterloo, 1977), pp. 341-355, Academic Press, 1979]) asserts that every bridgeless cubic…

This is part of an ongoing program to classify maximal orders on surfaces via their ramification data. Del Pezzo and ruled orders have already been classified. In this paper, we classify numerically Calabi-Yau orders which are the…

We consider Calabi-Yau threefolds Y defined as smooth linear sections of the double cover of the quintic symmetric determinantal hypersurface in P^{14}. In our previous works, we have shown that these Calabi-Yau threefolds Y are naturally…

In this paper, we prove the Bloch-Beilinson conjecture for certain abelian surfaces over $\mathbb{Q}$, provided that the BSD is known for these abelian surfaces.

The simple loop conjecture for 3-manifolds states that every 2-sided immersion of a closed surface into a 3-manifold is either injective on fundamental groups or admits a compression. This can be viewed as a generalization of the Loop…

The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X,Y) of Calabi-Yau threefolds, the best-understood mirror statements relate certain small corners of the moduli spaces of X…

We prove that the bounded derived category of the incidence algebra of the Tamari lattice is fractionally Calabi-Yau, giving a positive answer to a conjecture of Chapoton. The proof involves a combinatorial description of the Serre functor…

We study the symplectic analogue of log Calabi-Yau surfaces and show that the symplectic deformation classes of these surfaces are completely determined by the homological information.

While the earliest applications of AI methodologies to pure mathematics and theoretical physics began with the study of Hodge numbers of Calabi-Yau manifolds, the topology type of such manifold also crucially depend on their intersection…

There is a large number of different ways of constructing Calabi-Yau manifolds, as well as related non-geometric formulations, relevant in string compactifications. Showcasing this diversity, we discuss explicit deformation families of…

This paper expands on a remark in the paper "Mirror Symmetry for Log Calabi-Yau Surfaces I" of the first three authors of this paper, explaining fully how various constructions of the authors apply to give the mirror to the cubic surface.…

This is a survey on the project `Decorated Marked Surfaces', where we introduce the decoration $\Delta$ on a marked surfaces $\mathbf{S}$, to study Calabi-Yau-2 (cluster) categories, Calabi-Yau-3 (Fukaya) categories, braid groups for…

This is a short expository note about Calabi-Yau manifolds and degenerations of their Ricci-flat metrics.

We give an explicit estimate of the area of a closed surface by the diameter and a lower bound of curvature. This is better than Calabi-Cao's estimate for a nonnegatively curved two-sphere.

We consider examples of extremal transitions between families of Calabi-Yau complete intersection threefolds in toric varieties, which are induced by toric embeddings of one toric variety into the other. We show that the toric map induced…

We describe an efficient, construction independent, algorithmic test to determine whether Calabi--Yau threefolds admit a structure compatible with the Large Volume moduli stabilization scenario of type IIB superstring theory. Using the…

We study quivers supporting twisted graded Calabi-Yau algebras, building on work of Rogalski and the first author. Specifically, we classify quivers on four vertices in which the Nakayama automorphism acts on the degree zero part by either…

We associate a ring R to a log Calabi-Yau pair (X,D) or a degeneration of Calabi-Yau manifolds X->B. The vector space underlying R is determined by the tropicalization of (X,D) or X->B, while the product rule is defined using punctured…

In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of…

We prove Kontsevich's homological mirror symmetry conjecture for a large class of mirror pairs of Calabi--Yau hypersurfaces in toric varieties. These mirror pairs were constructed by Batyrev from dual reflexive polytopes. The theorem holds…