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We define a cobordism category of topological manifolds and prove that if $d \neq 4$ its classifying space is weakly equivalent to $\Omega^{\infty -1} MTTop(d)$, where $MTTop(d)$ is the Thom spectrum of the inverse of the canonical bundle…

Algebraic Topology · Mathematics 2025-03-14 Mauricio Gomez Lopez , Alexander Kupers

In this paper we study holomorphically homogeneous model submanifolds CR-type (1, 3) complex space $\mathbb C^4$. One finds moduli space of five-dimensional model surfaces Bloom-Graham type ((2, 1), (3, 1), (4, 1)). It is shown that there…

Complex Variables · Mathematics 2024-05-15 Ilya Zavolokin

A minimal homogeneous generating system of the algebra of semi-invariants of tuples of two-by-two matrices over an infinite field of characteristic two or over the ring of integers is given. In an alternative interpretation this yields a…

Commutative Algebra · Mathematics 2020-01-01 M. Domokos

In this paper we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3…

Mathematical Physics · Physics 2009-12-15 Fabio Bernardoni , Sergio L. Cacciatori , Bianca L. Cerchiai , Antonio Scotti

Let $k$ be a field of characteristic zero and $R$ a $k$-algebra. In this paper we study homogeneous $R$-lnds $D$ on $R[X,Y,Z]$ with respect to the standard weights $(1,1,1)$. We show that when $R$ is a PID, $rank(D)$ can be at most $2$ if…

Commutative Algebra · Mathematics 2024-03-22 Parnashree Ghosh

In this article we obtain a complete description of the congruences of lines in $\p^4$ of order one provided that the fundamental surface $F$ is non-reduced (and possibly reducible) at one of its generic points, and their classification…

Algebraic Geometry · Mathematics 2007-05-23 Pietro De Poi

We show that up to automorphisms of $\mathbb{P}^2_{\mathbb C}$ there are $5$ homogeneous convex foliations of degree four on $\mathbb{P}^2_{\mathbb C}.$ Using this result, we give a partial answer to a question posed in $2013$ by D.…

Differential Geometry · Mathematics 2018-12-11 Samir Bedrouni , David Marín

This work concerns the problem of relating characteristic numbers of one-dimensional holomorphic foliations of P^n to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional…

Complex Variables · Mathematics 2016-09-07 Marcio G. Soares

A cohomogeneity one manifold is a manifold with the action of a compact Lie group, whose quotient is one dimensional. Such manifolds are of interest in Riemannian geometry, in the context of nonnegative sectional curvature, as well as in…

Differential Geometry · Mathematics 2007-12-11 Corey A. Hoelscher

In this paper, we introduce notions of partitionability and characteristic sets of homogeneous polynomials and give a complete classification of groups faithfully acting on smooth cubic fivefolds. Specifically, we prove that there exist 20…

Algebraic Geometry · Mathematics 2024-08-15 Song Yang , Xun Yu , Zigang Zhu

In this paper we study the invariant Walker structures over the conformally flat four-dimensional homogeneous manifolds according to the Seger types of the Ricci operator.

Differential Geometry · Mathematics 2015-01-13 M. Chaichi , A. Zaeim , Y. Keshavarzi

We classify the non-degenerate homogeneous hypersurfaces in real and complex affine four-space whose symmetry group is at least four-dimensional.

Differential Geometry · Mathematics 2007-05-23 Michael Eastwood , Vladimir Ezhov

We study invariant divisors on the total spaces of the homogeneous deformations of rational complexity-one T-varieties constructed by Ilten and Vollmert. In particular, we identify a natural subgroup of the Picard group for any general…

Algebraic Geometry · Mathematics 2015-08-26 Andreas Hochenegger , Nathan Owen Ilten

We propose a novel sufficient condition establishing that a piecewise affine variety has the same topology as a variety of the sphere $\mathbb{S}^n$ defined by positively homogeneous $C^1$ functions. This covers the case of $C^1$ varieties…

Algebraic Geometry · Mathematics 2023-03-27 Christophe Raffalli

This paper studies modular forms of rank four and level one. There are two possiblities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we…

Number Theory · Mathematics 2018-10-23 Cameron Franc , Geoff Mason

We show some results of compact Kahler manifolds with elliptic homotopy type. In complex dimension 4 we list the Hodge diamonds of compact Kahler manifolds with elliptic homotopy type. In general dimension we obtain a partial…

Algebraic Topology · Mathematics 2022-08-16 Yang Su , Jianqiang Yang

In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles and Ulrich bundles on rational homogeneous spaces. %with respect to general polarizations. From this result, we see that there are only finitely many…

Algebraic Geometry · Mathematics 2023-11-06 Xinyi Fang

In this paper, the results in [Singular Hessians, J. Algebra 282 (2004), no. 1, 195--204], for polynomial Hessians with determinant zero in small dimensions $r+1$, are generalized to similar results in arbitrary dimension, for polynomial…

Algebraic Geometry · Mathematics 2022-03-18 Michiel de Bondt

A conjecture of Pukhlikov states that a smooth Fano variety of dimension at least four and index one is birationally rigid. We show that a general member of the linear system given by the ample generator of the Picard group of the moduli…

Algebraic Geometry · Mathematics 2007-05-23 Ana-Maria Castravet

Let $\mathbb{F}$ be a field of characteristic different from $2$ and $3$, and let $V$ be a vector space of dimension $2$ over $\mathbb{F}$. The generic classification of homogeneous quadratic maps $f\colon V\to V$ under the action of the…

Representation Theory · Mathematics 2022-09-27 R. Durán Díaz , L. Hernández Encinas , J. Muñoz Masqué