ODTÜ-BÝLKENT Algebraic Geometry Seminar
(See all past talks
ordered according to speaker and date)

2013 Fall Talks

1. ODTU, 4 October 2013, Friday, 15:40

Mesut Þahin-[Karatekin] - Affine toric varieties, cones, lattices, semigroup rings, toric ideals

 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.

2. Bilkent, 11 October 2013, Friday, 15:40

Mesut Þahin-[Karatekin] - Fans, toric variety of a fan via gluing affine toric varieties, Orbit-Cone correspondence

 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 Bayramý.

3. ODTU, 25 October 2013, Friday, 15:40

Mustafa Kalafat-[Tunceli] - Examples. Blow ups. Resolution of Singularities. Torus action. Orbits. Divisors.

 Abstract: We will revise the material on toric varieties with emphasis on examples and introduce some new concepts as time permits.

4. Bilkent, 1 November 2013, Friday, 15:40

Mustafa Kalafat-[Tunceli]- Blow ups. Resolution of Singularities. Torus action. Orbits. Divisors - I

 Abstract:  We will continue to discuss the material in Brasselet's exposition  "Geometry of toric varieties", sections 5 and 6, as time permits.

5. ODTU, 8 November 2013, Friday, 15:40

Mustafa Kalafat-[Tunceli]- Blow ups. Resolution of Singularities. Torus action. Orbits. Divisors - II

 Abstract:  We will complete our discussion of the material in Brasselet's exposition  "Geometry of toric varieties", sections 5 and 6.

6. Býlkent, 15 November 2013, Friday, 15:40

Mustafa Kalafat-[Tunceli]- Blow ups. Resolution of Singularities. Torus action. Orbits. Divisors - III

 Abstract:  We will complete our discussion with more examples.

7. ODTU, 29 November 2013, Friday, 15:40

Alexander Degtyarev-[Bilkent] - Resolutions of singularities, Viro’s patchworking, and tropical geometry

 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.

8. Bilkent, 6 December 2013, Friday, 15:40

Mesut Þahin-[Karatekin] - Projective toric varieties

 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 $X_A$.

9. ODTU, 13 December 2013, Friday, 15:40

Alexander Degtyarev-[Bilkent] - Viro's patchworking

 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.

10. Bilkent, 20 December 2013, Friday, 15:40

Mesut Þahin-[Karatekin] - Coordinate ring of a toric variety I

 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.

11. ODTU, 27 December 2013, Friday, 15:40

Mesut Þahin-[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 Ýkeda 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)