相关论文: Appendix to "The Chow rings of generalized Grassma…
The purpose of this paper is to extend the scope of the Ehrhart theory to periodic graphs. We give sufficient conditions for the growth sequences of periodic graphs to be a quasi-polynomial and to satisfy the reciprocity laws. Furthermore,…
We study the Chow ring of the moduli stack $\mathfrak{M}_{g,n}$ of prestable curves and define the notion of tautological classes on this stack. We extend formulas for intersection products and functoriality of tautological classes under…
We give an elementary theory of Henselian local rings and construct the Henselization of a local ring. All our theorems have an algorithmic content.
In this addendum we generalize some results of our article "Generically split projective homogeneous varieties", Duke Math. J. 152 (2010), no. 1, 155-173. More precisely, we remove all restrictions on the characteristic of the base field…
In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed fields, and the…
Chow varieties are a parameter space for cycles of a given variety of a given codimension and degree. We construct their analog for differential algebraic varieties with differential algebraic subvarieties, answering a question of Gao, Li…
Chow rings of toric varieties, which originate in intersection theory, feature a rich combinatorial structure of independent interest. We survey four different ways of computing in these rings, due to Billera, Brion, Fulton--Sturmfels, and…
The present note generalizes Debarre's Bertini-type results for in- verse images of Schubert varieties with the extension of formal func- tions.
A concise presentation of Schrodinger's ancilla theorem (1936 Proc. Camb. Phil. Soc. 32, 446) and its several recent rediscoveries.
We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a…
This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].
We give a revision of the proof of a Mazur-Ulam theorem for generalized gyrovector spaces given in the paper "Generalized gyrovector spaces and a Mazur-Ulam theorem" published in Publ. Math. Debrecen, 87 (2015), 393--413.
An introduction to all the key ideas of Lazic's proof of the theorem on the finite generation of adjoint rings.
This addendum presents a relevant stronger consequence of the main theorem of the paper "Higher order stroboscopic averaged functions: a general relationship with Melnikov functions" [arXiv:2011.03663], EJQTDE No. 77 (2021).
In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.
This paper gives additional background in algebraic geometry as an accompaniment to the article, ``Formal Groups, Elliptic Curves, and some Theorems of Couveignes'' [arXiv:math.NT/9708215]. Section 1 discusses the addition law on elliptic…
We show a Riemann-Roch theorem for group ring bundles over an arithmetic surface; this is expressed using the higher adeles of Beilinson-Parshin and the tame symbol via a theory of adelic equivariant Chow groups and Chern classes. The…
After recalling several constructions of the moduli space of curves of genus zero by different people we give our alternative construction of the moduli space. This gives a simple description of the intersection ring of this space. We give…
This manuscript is intended as an accompaniment to Guth's "A restriction estimate using polynomial partitioning". We begin by summarizing the core ideas of the proof, elaborating the history and development of the techniques therein. From…
We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.