ODTÜBÝLKENT
Algebraic Geometry Seminar
(See all past talks
ordered according to speaker
and date)
**** 2018 Fall Talks ****

Ali Sinan Sertöz[Bilkent]
 K3 covers of Enriques surfaces
Abstract: I last talked
on this subject on 2001 when I talked about Keum's
1990 work on the problem. There has been some
activity on the subject since then which I want to
talk about. I will explain the problem and
summarize what has been done so far and prepare
the audience for the next two talks where the
speakers will explain their most recent
contributions to the subject. 
Serkan Sonel[Bilkent ]
 K3 covers of Enriques surfaces with
Picard rank 18 and 19
Abstract: In this talk,
we partially determine the necessary and
sufficient conditions on the entries of the
intersection matrix of the transcendental lattice
of algebraic K3 surface with Picard number 18 ≤
ρ(X) ≤ 19 for the surface to doubly cover an
Enriques surface. 
Ođuzhan Yörük[Bilkent]
 Parity arguments on K3 covers of
Enrique surfaces with Picard rank 19
Abstract: Last two talks
of the seminar were mostly on the theoretical
parts of the subject. This time, we introduce some
computational arguments by using equivalence of
parities of the transcendental lattice of K3
surfaces, right after a brief reminding of what
was talked on previous two talks to warm up. Then,
we will apply this idea to reduce the number of
cases and time spent on showing which K3 surfaces
of Picard number 18 &19 cover an Enriques
surface. 
Alexander Degtyarev[Bilkent]
 A few further remarks on Enriques
surfaces
Abstract: I will
continue the subject of the previous talks, viz. a
characterization of the K3surfaces covering an
Enriques surface. I will: 
Emre Coţkun[ODTÜ] 
Serre's GAGA (Géometrie Algébrique et
Géométrie Analytique)
Abstract: Serre's famous
theorem known as "GAGA" (Géometrie Algébrique et
Géométrie Analytique  Algebraic Geometry and
Analytic Geometry) is a fundamental result in
algebraic geometry. It basically says that the
theory of complex analytic subvarieties of
projective space and the theory of algebraic
subvarieties of projective space coincide. In this
series of lectures, we shall start with the
fundamentals of complex analytic geometry and then
move toward the proof of GAGA. 
Emre Coţkun[ODTÜ] 
Serre's GAGAII
Abstract: Serre's famous
theorem known as "GAGA" (Géometrie Algébrique et
Géométrie Analytique  Algebraic Geometry and
Analytic Geometry) is a fundamental result in
algebraic geometry. It basically says that the
theory of complex analytic subvarieties of
projective space and the theory of algebraic
subvarieties of projective space coincide. In this
series of lectures, we shall start with the
fundamentals of complex analytic geometry and then
move toward the proof of GAGA. 
Emre Coţkun[ODTÜ] 
Serre's GAGAIII
Abstract: Serre's famous
theorem known as "GAGA" (Géometrie Algébrique et
Géométrie Analytique  Algebraic Geometry and
Analytic Geometry) is a fundamental result in
algebraic geometry. It basically says that the
theory of complex analytic subvarieties of
projective space and the theory of algebraic
subvarieties of projective space coincide. In this
series of lectures, we shall start with the
fundamentals of complex analytic geometry and then
move toward the proof of GAGA. 
Yýldýray Ozan[ODTÜ] 
Manifolds Admitting No Real Projective
Structure
Abstract: In this talk
first, we will define and give basic results about
real projective structures on smooth
manifolds. Then we will discuss such
structures on two and three manifolds. Next we
will mention the 2015 result by D. Cooper and W.
Goldman that the smooth manifold ${\mathbb{R}P}^{3}\mathrm{\u266f}{\mathbb{R}P}^{3}$
does not admit
any real projective structure (the first known
example in dimension three), and we will
generalize this result to all higher
dimensions. If time permits, we will mention
different type of examples of smooth manifolds
with no real projective structure. 
Nil Ţahin[Bilkent] 
One dimensional Gorenstein Local Rings with
decreasing Hilbert Function
Abstract: In this talk,
starting from Rossi's conjecture stating "Hilbert
function of a one dimensional Gorenstein Local
Ring is nondecreasing", I will give a little
history of the recent works in this subject and
talk about Oneto, Strazzanti and Tamone's work
that constructs infinitely many onedimensional
Gorenstein Local rings that decreases at some
level. 
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
Abuilding at Bilkent.
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