Related papers: Twisted Milnor Hypersurface I

We present the twisted covariant form hierarchies (TCFHs) of warped (massive) IIA AdS backgrounds. As a consequence we demonstrate that all Killing spinor form bilinears satisfy a generalisation of the conformal Killing-Yano equation with…

Let $\mathcal{N}_*$ be the unoriented cobordism algebra, let $G=(\Z_2)^n$ and let $Z_*(G)$ denote the equivariant cobordism algebra of $G$-manifolds with finite stationary point sets. Let $\epsilon_* :Z_*(G) \to \mathcal{N}_*$ be the…

We construct the twistor space associated with an HKT manifold, that is, a hyper-K\"ahler manifold with torsion, a type of geometry that arises as the target space geometry in two-dimensional sigma models with (4,0) supersymmetry. We show…

We provide an explicit computation over the integers of the bar version $\overline{HM}_*$ of the monopole Floer homology of a three-manifold in terms of a new invariant associated to its triple cup product called extended cup homology. This…

The space spanned by the characters of twisted affine Lie algebras admit the action of certain congruence subgroups of $SL(2,\mathbb{Z})$. By embedding the characters in the space spanned by theta functions, we study an…

We derive a number of inequalities involving L\^e numbers of non-isolated hypersurface singularities. In particular, we derive L\^e-Iomdine formulas with inequalities and use these, together with Teissier's Minkowski inequalities for…

Our first result is that a homogeneous form $F$ in $n$ variables is GIT semistable with respect to the natural $SL(n)$-action if and only if the first non-trivial Hilbert point of the associated Milnor algebra is semistable. We also prove…

We give a gauge invariant characterisation of the elliptic affine sphere equation and the closely related Tzitz\'eica equation as reductions of real forms of $SL(3, \C)$ anti--self--dual Yang--Mills equations by two translations, or…

We show that the Hirzebruch-Milnor class of a projective hypersurface, which gives the difference between the Hirzebruch class and the virtual one, can be calculated by using the Steenbrink spectra of local defining functions of the…

We use classical invariant theory to construct invariants of complex graded Gorenstein algebras of finite vector space dimension. As a consequence, we obtain a way of extracting certain numerical invariants of quasi-homogeneous isolated…

Block and G\"ottsche have defined a $q$-number refinement of counts of tropical curves in $\mathbb{R}^2$. Under the change of variables $q=e^{iu}$, we show that the result is a generating series of higher genus log Gromov-Witten invariants…

We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance we prove a…

Let $W$ be a finite Coxeter group. We give an algebraic presentation of what we refer to as ``the non-crossing algebra'', which is associated to the hyperplane complement of $W$ and to the cohomology of its Milnor fibre. This is used to…

Consider an asymptotically flat Riemannian manifold $(M,g)$ of dimension $n \geq 3$ with nonempty compact boundary. We recall the harmonic conformal class $[g]_h$ of the metric, which consists of all conformal rescalings given by a harmonic…

We use the manifestly conformally invariant description of a Lorentzian conformal structure in terms of a parabolic Cartan geometry in order to introduce a superalgebra structure on the space of twistor spinors and normal conformal vector…

We develop variation formulas on almost-product (e.g. foliated) pseudo-Riemannian manifolds, and we consider variations of metric preserving orthogonality of the distributions. These formulae are applied to Einstein-Hilbert type actions:…

Our aim is to study invariant hypersurfaces immersed in the Euclidean space $\mathbb{R}^{n+1}$, whose mean curvature is given as a linear function in the unit sphere $\mathbb{S}^n$ depending on its Gauss map. These hypersurfaces are closely…

We study certain DT invariants arising from stable coherent sheaves in a nonsingular projective threefold supported on the members of a linear system of a fixed line bundle. When the canonical bundle of the threefold satisfies certain…

The main result of this paper is an expression of the flag curvature of a submanifold of a Randers-Minkowski space $({\mathscr V},F)$ in terms of invariants related to its Zermelo data $(h,W)$. More precisely, these invariants are the…

We introduce a notion of the twist of an isometry of the hyperbolic plane. This twist function is defined on the universal covering group of orientation-preserving isometries of the hyperbolic plane, at each point in the plane. We relate…