[Turkmath:5471] ODTU-Bilkent Algebraic Geometry Seminar-Zoom-504

[Ali Sinan Sertöz]

*
*
*Welcome to the 2022 Spring talks of ODTU-Bilkent Algebraic Geometry 
Seminars**
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**
/since 2000/
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This week the ODTU-Bilkent Algebraic Geometry Seminar 
<http://www.bilkent.edu.tr/%7Esertoz/agseminar.htm>  is *Online.*

/This talk will begin at _*15:40*__(GMT+3)_/

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**//
Georgi Petrov
Return to the past
/(from the artist's homepage)/
**Speaker:Alexander Degtyarev
**
**Affiliation:Bilkent
Title:Towards 800 conics on a smooth quartic surfaces

**
**Abstract:**This will be a technical talk where I will discuss a few 
computational aspects of my work in progress towards the following 
conjecture.

Conjecture: A smooth quartic surface in P3 may contain at most 800 conics.

I will suggest and compare several arithmetical reductions of the 
problem. Then, for the chosen one, I will discuss a few preliminary 
combinatorial bounds and some techniques used to handle the few cases 
where those bounds are not sufficient.

At the moment, I am quite confident that the conjecture holds. However, 
I am trying to find all smooth quartics containing 720 or more conics, 
in the hope to find the real quartic maximizing the number of  real 
lines and to settle yet another conjecture (recall that we count all 
conics, both irreducible and reducible).

Conjecture: If a smooth quartic X⊂P3 contains more than 720 conics, then 
X has no lines; in particular, all conics are irreducible.

Currently, similar bounds are known only for sextic K3-surfaces in P4.

As a by-product, I have found a few examples of large configurations of 
conics that are not Barth--Bauer, i.e., do not contain
a 16-tuple of pairwise disjoint conics or, equivalently, are not Kummer 
surfaces with all 16 Kummer divisors conics./
///
*Date:11 March 2022*, Friday
*Time: 15:40 /(GMT+3)/*
*Place: **Zoom
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    **One day before the seminar, an announcement with the Zoom meeting
    link will be sent to those who registered with Sertöz.
    **

    **If you have registered before for one of the previous talks, there
    is no need to register again; you will automatically receive a link
    for this talk too.
    **

    **If you have not registered before, please contact him at
    sertoz at bilkent.edu.tr
    <mailto:sertoz at bilkent.edu.tr?subject=Zoom%20Seminar%20Address%20Request>.**

**


Please bring your own tea and cookies and self-serve at the convenience 
of your own home! 😁

You are most cordially invited to attend.

Ali Sinan Sertöz
**

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Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Turkey
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
Fax: (90)-(312) - 290 1797
e-mail:sertoz at bilkent.edu.tr  <mailto:sertoz at bilkent.edu.tr>  
Web:sertoz.bilkent.edu.tr  <http://sertoz.bilkent.edu.tr>  
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