Related papers: Orbital degeneracy loci and applications

In [BFMT17] we introduced orbital degeneracy loci as generalizations of degeneracy loci of morphisms between vector bundles. Orbital degeneracy loci can be constructed from any stable subvariety of a representation of an algebraic group. In…

Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in…

We define a new symmetry for morphisms of vector bundles, called triality symmetry, and compute Chern class formulas for the degeneracy loci of such morphisms. In an appendix, we show how to canonically associate an octonion algebra bundle…

We study resolutions of singularities of orbit closures in quiver representations. We consider certain resolutions of singularities which have already been constructed by Reineke, and we determine under which conditions they are crepant.…

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit closures on the flag variety $G/B$, where $G = GL(n,\C)$, and where $K$ is one of…

This paper presents a rigidity property of the exceptional locus of some kind of small birational contractions. An application in the context of geometric transitions and Calabi-Yau threefolds moduli space is then given, with some physical…

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit closures on the flag variety $G/B$ for various symmetric pairs $(G,K)$. In type…

We consider the variety of Filippov ($n$-Lie) algebra structures on an $(n+1)$-dimensional vector space. The group $GL_n(K)$ acts on it, and we study the orbit closures with respect to the Zariski topology. This leads to the definition of…

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our…

Let S be a smooth projective surface over the complex field. Under certain technical assumptions, we prove that the degeneracy locus of the universal sheaf over the moduli space of stable sheaves is either empty or an irreducible…

Given a map of vector bundles on a smooth variety, consider the deepest degeneracy locus where its rank is smallest. We show it carries a natural perfect obstruction theory whose virtual cycle can be calculated by the Thom-Porteous formula.…

We introduce and study the maximal-variation locus in families and moduli spaces of projective curves, defined via conductor-level balancing of meromorphic differentials on the normalization. This notion captures precisely when the space of…

We study connectedness of degeneracy loci $D_{r-k}(\varphi)$ of morphisms $\varphi : {\mathcal O}_X^{\oplus (r+1-k)} \to \mathcal E$, where $\mathcal E$ is a rank $r$ globally generated bundle on a smooth $n$-dimensional variety $X$ and $k…

We give explicit formulas for torus-equivariant fundamental classes of closed $K$-orbits on the flag variety $G/B$ when $G$ is one of the classical groups $SL(n,\C)$, $SO(n,\C)$, or $Sp(2n,\C)$, and $K$ is a symmetric subgroup of $G$. We…

We use the method of stable degenerations to study the local geometry of Calabi-Yau fourfolds for F-theory compactifications dual to heterotic compactifications on a Calabi-Yau threefold with fivebranes wrapping holomorphic curves in the…

We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal…

We prove that the Hilbert scheme of degeneracy loci of pairs of global sections of Omega(2), the twisted cotangent bundle on P^(n-1), is unirational and dominated by the Grassmannian of lines in the projective space of skew-symmetric forms…

Let V be a rank N vector bundle on a d-dimensional complex projective scheme X; assume that V is equipped with a quadratic form with values in a line bundle L and that S^2 V^* \otimes L is ample. Suppose that the maximum rank of the…

Let V be a smooth equidimensional quasi-affine variety of dimension r over the complex numbers $C$ and let $F$ be a $(p\times s)$-matrix of coordinate functions of $C[V]$, where $s\ge p+r$. The pair $(V,F)$ determines a vector bundle $E$ of…

We study topological properties of families of Hamiltonians which may contain degenerate energy levels aka. band crossings. The primary tool are Chern classes, Berry phases and slicing by surfaces. To analyse the degenerate locus, we study…