相关论文: Krichever Correspondence for Algebraic Surfaces
Recently Krichever proposed a generalization of the amoeba and the Ronkin function of a plane algebraic curve. In our paper higher-dimensional version of this generalization is studied. We translate to the generalized case different…
In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme…
We construct a new class of N-dimensional Lie algebras and apply them to integrable systems. In this paper, we obtain a nonisospectral KdV integrable hierarchy by introducing a nonisospectral spectral problem. Then, a coupled nonisospectral…
This paper investigates wave-equations on spacetimes with a metric which is locally analytic in the time. We use recent results in the theory of the non-characteristic Cauchy problem to show that a solution to a wave-equation vanishing in…
These notes are an introduction to and an overview of the theory of algebraic surfaces over algebraically closed fields of positive characteristic. After some background in characteristic-p-geometry, we sketch the Kodaira-Enriques…
We study the differential properties of generalized arc schemes, and geometric versions of Kolchin's Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.
We classify meromorphic affine connections on compact complex surfaces with algebraic dimension one, extending the work of Inoue,Kobayashi and Ochiai (1981) in the holomorphic case. The motivation is to investigate possible extension of the…
One of the major open problems in noncommutative algebraic geometry is the classification of noncommutative projective surfaces (or, slightly more generally, of noetherian connected graded domains of Gelfand-Kirillov dimension 3). Earlier…
An algebraic construction more general and intimately connected with that of Faddeev$^1$, along with its application for generating different classes of quantum integrable models are summarised to complement the recent results of ref. 1 (…
I give a conjectural generating function for the numbers of $\delta$-nodal curves in a linear system of dimension $\delta$ on an algebraic surface. It reproduces the results of Vainsencher for the case $\delta\le 6$ and Kleiman-Piene for…
Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan…
We describe explicitly the algebras of degree zero operations in connective and periodic p-local complex K-theory. Operations are written uniquely in terms of certain infinite linear combinations of Adams operations, and we give formulas…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We establish a structure theorem on the arc space of a $k$-scheme of finite type. More precisely, we show that the arc space is locally for the pro-smooth toplogy a product of an infinite dimensional affine space and of a non-noetherian…
We introduce a hierarchy of mutually commuting dynamical systems on a finite number of Laurent series. This hierarchy can be seen as a prolongation of the KP hierarchy, or a ``reduction'' in which the space coordinate is identified with an…
We define and analyse the properties of contact Lie systems, namely systems of first-order differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of…
k-Contact geometry is a generalisation of contact geometry to analyse field theories. We develop an approach to k-contact geometry based on distributions that are distributionally maximally non-integrable and admit, locally, k commuting…
This article is an interdisciplinary review and an on-going progress report over the last few years made by myself and collaborators in certain fundamental subjects on two major theoretic branches in mathematics and theoretical physics:…
These are notes on some algebraic geometry of complex projective curves, together with an application to studying the contact curves in CP^3 and the null curves in the complex quadric Q^3 in CP^4, related by the well-known Klein…
In this paper, we show a local energy convexity of $W^{1,2}$ maps into $CAT(K)$ spaces. This energy convexity allows us to extend Colding and Minicozzi's width-sweepout construction to produce closed geodesics in any closed Alexandrov space…