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We give a complete classification of P1-bundles over a projective manifold of Picard number one which admit another smooth morphism of relative dimension one.

Algebraic Geometry · Mathematics 2013-01-08 Kiwamu Watanabe

We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension…

Commutative Algebra · Mathematics 2009-09-18 Dima Trushin

This article discusses the existence problem of a compact quotient of a symmetric space by a properly discontinuous group with emphasis on the non-Riemannian case. Discontinuous groups are not always abundant in a homogeneous space $G/H$ if…

Differential Geometry · Mathematics 2011-06-22 Toshiyuki Kobayashi , Taro Yoshino

Let $\mathbb X\subset\mathbb P(V)$ be a projective variety, which is not contained in a hyperplane. Then every vector $v$ in $V$ can be written as a sum of vectors from the affine cone $X$ over $\mathbb X$. The minimal number of summands in…

Algebraic Geometry · Mathematics 2015-04-07 A. Petukhov , V. Tsanov

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we…

Algebraic Geometry · Mathematics 2008-09-26 Alessandro Ruzzi

Let $P$ be a commutative Noetherian ring and $F$ be a self-dual acyclic complex of finitely generated free $P$-modules. Assume that $F$ has length four and $F_0$ has rank one. We prove that $F$ can be given the structure of a Differential…

Commutative Algebra · Mathematics 2021-03-17 Andrew R. Kustin

We give details of a new isolated symplectic singularity found in an affine chart in a crepant partial resolution of $\mathbb{C}^4/G_5$, which is 4-dimensional, isolated, and locally simply-connected. We distinguish the new singularity…

Algebraic Geometry · Mathematics 2025-06-02 Callum Berry

In this paper, we prove that a smooth projective globally $F$-split variety with numerically flat tangent bundle is an \'etale quotient of an ordinary abelian variety. We also show its logarithmic analog, which contains a characterization…

Algebraic Geometry · Mathematics 2023-03-20 Sho Ejiri , Shou Yoshikawa

An intriguing correspondence between four-qubit systems and simple singularity of type $D_4$ is established. We first consider an algebraic variety $X$ of separable states within the projective Hilbert space…

Mathematical Physics · Physics 2015-06-18 Frédéric Holweck , Jean-Gabriel Luque , Michel Planat

Let X be a Q-factorial Gorenstein Fano variety. Suppose that the singularities of X are canonical and that the locus where they are non-terminal has dimension zero. Let D be a prime divisor of X. We show that rho_X - rho_D < 9 (where rho is…

Algebraic Geometry · Mathematics 2012-12-05 Gloria Della Noce

For a smooth, projective family of homogeneous varieties defined over a number field, we show that if potential density holds for the rational points of the base, then it also holds for the total space. A conjecture of Campana and…

Algebraic Geometry · Mathematics 2011-02-22 J. -L. Colliot-Thélène , J. N. Iyer

Let $\phi: X \to \mathbb P^n$ be a double cover branched along a smooth hypersurface of degree $2m, 2 \leq m \leq n-1$. We study the varieties of minimal rational tangents $\mathcal C_x \subset \mathbb P T_x(X)$ at a general point $x$ of…

Algebraic Geometry · Mathematics 2013-04-01 Jun-Muk Hwang , Hosung Kim

We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat…

Differential Geometry · Mathematics 2021-10-11 Mohamad Chaichi , Yadollah Keshavarzi

Consider a family f:A --> U of g-dimensional abelian varieties over a quasiprojective manifold U. Suppose that the induced map from U to the moduli scheme of polarized abelian varieties is generically finite and that there is a projective…

Algebraic Geometry · Mathematics 2009-10-12 Martin Moeller , Eckart Viehweg , Kang Zuo

Let $X$ be a nonsingular complex projective toric variety. We address the question of semi-stability as well as stability for the tangent bundle $T{X}$. In particular, a complete answer is given when $X$ is a Fano toric variety of dimension…

Algebraic Geometry · Mathematics 2021-12-17 Indranil Biswas , Arijit Dey , Ozhan Genc , Mainak Poddar

We argue that there are two distinct classes of type I compactification to four dimensions on any space. These two classes are distinguished in a mysterious way by the presence (or absence) of a discrete 6-form potential. In simple…

High Energy Physics - Theory · Physics 2009-11-07 David R. Morrison , Savdeep Sethi

Let F,G in C[x_1,...,x_n] be two polynomials in n variables x_1,...,x_n over the complex numbers field C. In this paper, we prove that if the degree of the Poisson bracket [F,G] is small enough then there are strict constraints for…

Commutative Algebra · Mathematics 2021-01-26 Daria Holik , Marek Karaś

We show how to construct certain homogeneous deformations for rational normal varieties with codimension one torus action. This can then be used to construct homogeneous deformations of any toric variety in arbitrary degree. For locally…

Algebraic Geometry · Mathematics 2012-11-20 Nathan Owen Ilten , Robert Vollmert

Let X be a complete toric variety with homogeneous coordinate ring S. In this article, we compute upper and lower bounds for the codimension in the critical degree of ideals of S generated by dim(X)+1 homogeneous polynomials that don't…

Algebraic Geometry · Mathematics 2007-05-23 David Cox , Alicia Dickenstein

Let X be a Fano manifold with Picard number one such that the tangent bundle T_X is big. If X admits a rational curve with trivial normal bundle, we show that X is isomorphic to the del Pezzo threefold of degree five.

Algebraic Geometry · Mathematics 2021-10-15 Andreas Höring , Jie Liu
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