Related papers: Algebraic structures with unbounded Chern numbers

Given a smooth complex variety $X$, an algebraically skew embedding of $X$ is an embedding of $X$ into a complex projective space $\mathbb{P}^N$ such that for any two points $x,y\in X$, their embedded tangent spaces in $\mathbb{P}^N$ do not…

In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occurring for a projection of a smooth curve embedded by a…

We show that any smooth and proper dg-algebra (over some base ring k) is determined, up to quasi-isomorphism, by its underlying A_n-algebra, for a certain integer n. Similarly, any morphism between two smooth and proper dg-algebras is…

We give algebraic and geometric classifications of complex $4$-dimensional nilpotent noncommutative Jordan algebras. Specifically, we find that, up to isomorphism, there are only $18$ non-isomorphic nontrivial nilpotent noncommutative…

We provide a bound on the dimension of Schur multiplier of a finite dimensional nilpotent Lie superalgebra which is more precise than the previous bounds on the dimension of Schur multiplier of Lie superalgebra.

We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…

We construct algebraic families of smooth affine $\mathbb{A}^1$-contractible varieties of every dimension $n\geq 4$ over fields of characteristic zero which are non-isomorphic to affine spaces and potential counterexamples to the Zariski…

This short note summarizes a number of facts about the ring $K^0(X)$ for $X$ a $4$-dimensional CW-complex. Unusual features of this dimension are that every complex vector bundle is determined up to stable isomorphism by its Chern classes,…

This note is concerned with the Rouquier dimension of the bounded derived category of coherent complexes on a Noetherian algebraic stack. Specifically, we study the diagonal dimension of a morphism, which can be used to produce upper bounds…

We derive a formula for the Chern classes of the bundles of conformal blocks on \bar{M}_{0,n} associated to simple finite dimensional Lie algebras and explore its consequences in more detail for sl_2 and in general for level 1. We also give…

Let $n=2,3,4,5$ and let $X$ be a smooth complex projective hypersurface of $\mathbb P^{n+1}$. In this paper we find an effective lower bound for the degree of $X$, such that every holomorphic entire curve in $X$ must satisfy an algebraic…

In this article we give a necessary and sufficient condition to characterize projective submanifolds in ${\mathbb P}^N$ with codimensions 2 and 3. The conditions involve the Chern classes of the manifold and a very ample line bundle on the…

In this paper, we obtain an explicit formula for the Chern character of a locally abelian parabolic bundle in terms of its constituent bundles. Several features and variants of parabolic structures are discussed. Parabolic bundles arising…

In the first part of this paper we study geometric formality for generalized flag manifolds, including full flag manifolds of exceptional Lie groups. In the second part we deal with the problem of the classification of invariant almost…

We address the problem of the maximal finite number of real points of a real algebraic curve (of a given degree and, sometimes, genus) in the projective plane. We improve the known upper and lower bounds and construct close to optimal…

We present in this article a family of new combinatorial identities via purely differential/complex geometry methods, which include as a speical case a unified and explicit formula for Chern numbers of all complex flag manifolds. Our…

It is known for scalar ordinary differential equations, and for systems of ordinary differential equations of order not higher than the third, that their Lie point symmetry algebras is of maximal dimension if and only if they can be reduced…

For central simple finitely generated algebras of finite Gelfand-Kirillov dimension and for their division algebras upper bounds are obtained for the transcendence degree of their commutative subalgebras and subfields respectively. In the…

We categorize all non-abelian nilpotent Lie superalgebras of dimension $(m|n)$, where $1\leq s(L)\leq 10$, and $s(L)$ is a non-negative integer defined by Nayak. Furthermore, we classify the structure of all Lie superalgebras of dimension…

We show that a proper algebraic n-dimensional scheme Y admits nontrivial vector bundles of rank n, even if Y is non-projective, provided that there is a modification containing a projective Cartier divisor that intersects the exceptional…