Related papers: Globally generated vector bundles on complete inte…
In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefold with h^{1,1}>1. We give examples of stable bundles of rank…
We prove the Shafarevich conjecture for varieties with globally generated cotangent bundle, subject to mild numerical conditions.
We systematically construct a large number of compact Calabi-Yau fourfolds which are suitable for F-theory model building. These elliptically fibered Calabi-Yaus are complete intersections of two hypersurfaces in a six dimensional ambient…
We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry…
Clifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in a previous paper of the authors. The present paper studies bundles which compute these Clifford indices. We show that under…
We establish the existence of rank two Ulrich vector bundles on surfaces that are either of maximal Albanese dimension or with irregularity 1, under many embeddings. In particular we get the first known examples of Ulrich vector bundles on…
We obtain a sharp bound on the degree of a globally generated vector bundle over a reduced irreducible projective variety defined over an algebraically closed field of characteristic zero. As an application, we obtain a Del Pezzo-Bertini…
As shown in a previous paper, certain naturally arising cones of holomorphic vector bundle sections over the main component $\ov\M_{1,k}^0(\P,d)$ of the moduli space of stable genus-one holomorphic maps into $\P$ have a well-defined euler…
We construct infinitely many complete Calabi-Yau metrics on $\mathbf{C}^n$ for $n \geq 3$, with maximal volume growth, and singular tangent cones at infinity. In addition we construct Calabi-Yau metrics in neighborhoods of certain isolated…
We study a class of graded algebras obtained from Ore extensions of graded Calabi-Yau algebras of dimension 2. It is proved that these algebras are graded Calabi-Yau and graded coherent. The superpotentials associated to these graded…
This is the second part of our ongoing project on the relations between Gopakumar-Vafa BPS invariants (GV) and quantum K-theory (QK) on the Calabi--Yau threefolds (CY3). We show that on CY3 a genus zero quantum K-invariant can be written as…
We prove that any rank two arithmetically Cohen-Macaulay vector bundle on a general hypersurface of degree at least three in $\mathbb{P}^5$ must be split.
We apply deep-learning techniques to the string landscape, in particular, $SO(32)$ heterotic string theory on simply-connected Calabi-Yau threefolds with line bundles. It turns out that three-generation models cluster in particular islands…
The Abel-Jacobi map of the family of elliptic quintics lying on a general cubic threefold is studied. It is proved that it factors through a moduli component of stable rank 2 vector bundles on the cubic threefold with Chern numbers c_1=0,…
In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on…
We classify nef vector bundles on a smooth quadric surface with first Chern class $(2,2)$ over an algebraically closed field of characteristic zero.
We compute genus-zero Gromov--Witten invariants of Calabi--Yau complete intersection 3-folds in Grassmannians using supersymmetric localization in A-twisted non-Abelian gauged linear sigma models. We also discuss a Seiberg-like duality…
We construct a full exceptional collection consisting of vector bundles in the derived category of coherent sheaves on the so-called Cayley Grassmannian, the subvariety of the Grassmannian $\mathrm{Gr}(3, 7)$ parameterizing 3-subspaces that…
We categorify various finite-type cluster algebras with coefficients using completed orbit categories associated to Frobenius categories. Namely, the Frobenius categories we consider are the categories of finitely generated Gorenstein…
Batyrev constructed a family of Calabi-Yau hypersurfaces dual to the first Chern class in toric Fano varieties. Using this construction, we introduce a family of Calabi-Yau manifolds whose SU-bordism classes generate the special unitary…