ODTÜ-BİLKENT Algebraic Geometry Seminar
(See all past talks
ordered according to speaker and
date)
2013 Fall Talks
|
Abstract: In this talk, we give the classical definition of a toric variety involving the torus action and provide examples to illustrate it. We introduce two important lattices that play important roles in the theory of algebraic tori and demonstrate how they arise naturally in the toric case. Finally, we introduce affine toric varieties determined by strongly convex rational cones. |
|
Abstract: In this talk, we introduce fans and the (abstract) toric variety determined by a fan via gluing affine toric varieties defined by the cones in the fan. We include some examples and conclude with the correspondence between orbits of the torus action and the cones in the fan. |
18 October is Kurban Bayramı.
|
Abstract: We will revise the material on toric varieties with emphasis on examples and introduce some new concepts as time permits. |
|
Abstract: We will continue to discuss the material in Brasselet's exposition "Geometry of toric varieties", sections 5 and 6, as time permits. |
|
Abstract: We will complete our discussion of the material in Brasselet's exposition "Geometry of toric varieties", sections 5 and 6. |
|
Abstract: We will complete our discussion with more examples. |
21-24 Nov
2013 Japanese Turkish Joint Geometry Meeting, Galatasaray University, İstanbul
|
Abstract: In this very introductory talk I will try to discuss the interplay between such concepts as embedded toric resolutions of singularities via Newton polygons, Viro’s combinatorial patchworking, and tropical geometry. |
|
Abstract: We start with the definition of normal, very ample and smooth polytopes. We next define the projective toric variety $X_A$ determined by a finite set $A$ of lattice points. When $A$ is the lattice points of a polytope $P$ we demonstrate that $X_A$ reflects the properties of $P$ best if $P$ is very ample. We also define the normal fan of $P$ and discuss the relation between the corresponding "abstract" variety $X_P$ and the embedded variety $X_A$. |
|
Abstract: This is a continuation of my previous talk. After a brief introduction to Hilbert’s 16$^{\rm th}$ problem, I will try to outline the basic ideas underlying Viro’s method of patchworking real algebraic varieties. |
|
Abstract: The aim of this talk is to introduce the so called homogeneous coordinate ring of a normal toric variety. We will see how Chow group of Weil divisors turn this ring into a graded ring. Finally we show that every normal toric variety is a categorical quotient. |
ODTU, 27 December 2013, Friday, 15:40
Mesut Şahin-[Karatekin] - Coordinate
ring of a toric variety II
|
Abstract: After the promised example of "bad" quotient, I will review the correspondence between subschemes of a normal toric variety and multigraded ideals of its homogeneous coordinate ring. |
ODTÜ talks are either at Hüseyin
Demir
Seminar room or at Gündüz İkeda seminar room at the Mathematics building of ODTÜ.
Bilkent talks are at room 141 of Faculty of Science A-building at
Bilkent.
| 2000-2001 Talks (1-28) | 2001 Fall Talks (29-42) | 2002 Spring Talks (43-54) | 2002 Fall Talks (55-66) |
| 2003 Spring Talks (67-79) | 2003 Fall Talks (80-90) | 2004 Spring Talks (91-99) | 2004 Fall Talks (100-111) |
| 2005 Spring Talks (112-121) | 2005 Fall Talks (122-133) | 2006 Spring Talks (134-145) | 2006 Fall Talks (146-157) |
| 2007 Spring Talks (158-168) | 2007 Fall Talks (169-178) | 2008 Spring Talks (179-189) | 2008 Fall Talks (190-204) |
| 2009 Spring Talks (205-217) | 2009 Fall Talks (218-226) | 2010 Spring Talks (227-238) | 2010 Fall Talks (239-248) |
| 2011 Spring Talks (249-260) | 2011 Fall Talks (261-272) | 2012 Spring Talks (273-283) | 2012 Fall Talks (284-296) |
| 2013 Spring Talks (297-308) |