相关论文: Rationally connected varieties

This is a survey article, based on the author's lectures in the 2015 AMS Summer Research Institute in Algebraic Geometry, and to appear in the Proceedings.

We discuss a possible approach to the study of the vanishing of the Kobayashi pseudometric of a projective variety X, using chains of rational or elliptic curves contained in an arbitrarily small neighborhood of X in projective space for…

This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004. It is meant as an overview of recent…

In this note we classify simply connected rationally elliptic compact toric orbifolds up to algebraic isomorphism.

This paper begins the exploration of what we call measures of association between two irreducible complex projective varieties of the same dimension. The idea is to study from various points of view the minimal complexity of correspondences…

A short informal survey on the topics listed in the title. For the proceedings of the International Conference on Rings and Algebras X.

This is the author's 2004 Master's thesis at Iowa State University, done under the supervision of Roger D. Maddux. It provides a background in relation algebras. Three results from the literature are demonstrated in full: (i.) RRA is a…

This is an expository article, which contributes to the Proceedings of the conference "Groups of Automorphisms in Birational and Affine Geometry", held in Trento in 2012. We propose that (rational) fibrations on the projective space $\p^n$…

This is an expanded and updated version of a lecture series I gave at Seoul National University in September 1997. It is in some sense an update of the 1979 Griffiths and Harris paper with a similar title. I discuss: Homogeneous varieties,…

This is an expository paper which presents the holomorphic classification of rational complex surfaces from a simple and intuitive point of view, which is not found in the literature. Our approach is to compare this classification with the…

Notes from a talk at the April 2011 ICMS (Edinburgh) conference on the recent solution of the Kervaire invariant problem. This is an entirely expository account, emphasizing connections with the theory of topological automorphic forms.

In this paper we study varieties covered by rational or elliptic curves. First, we show that images of Calabi-Yau or irreducible symplectic varieties under rational maps are almost always rationally connected. Second, we investigate…

This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic…

In this paper, we proved two results regarding the arithmetics of separably $\mathbb{A}^1$-connected varieties of rank one. First we proved over a large field, there is an $\mathbb{A}^1$-curve through any rational point of the boundary, if…

We study zero cycles on rationally connected varieties defined over characteristic zero Laurent fields with algebraically closed residue fields. We show that the degree map induces an isomorphism for rationally connected threefolds defined…

This is a small note meant to be published in a Conference Proceedings. We discuss elementary rationality questions in the Grothendieck ring of varieties for the quotient of a finite dimensional vector space over a characteristic 0 field by…

This is an expository lecture, for the Abel bicentennial (Oslo, 2002), describing some recent work on the (small) quantum cohomology ring of Grassmannians and other homogeneous varieties.

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and…

Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent and the fibration method, in a number-theoretical context…

In this paper, we classify the possible group structures on the set of $R$-valued points of an abelian variety, where $R$ is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over…