[Turkmath:5262] ODTU-Bilkent Algebraic Geometry Seminar-Zoom-496

[Ali Sinan Sertöz]

*
*
*Welcome to the 2021 Fall 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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**//
/Paul Gauguin (1848-1903)
/

**Speaker:Alexander Degtyarev
**
**Affiliation: Bilkent
Title:Conics on polarized K3-surfaces

**
**Abstract:**  Generalizing Barth and Bauer, denote by N_2n(d) the 
maximal number of smooth degree d rational curves that can lie on a 
smooth 2n-polarized K3-surface X⊂Pn. Originally, the question was raised 
in conjunction with smooth spatial quartics, which are K3-surfaces.

The numbers N_2n(1) are well understood, whereas the only known value 
for d=2 is N_6(2)=285. I will discuss my recent discoveries that support 
the following conjecture on the conic counts in the remaining 
interesting degrees.

Conjecture. One has N_2(2)=8910, N_4(2)=800, and N_8(2)=176.

The approach used does not distinguish (till the very last moment) 
between reducible and irreducible conics. However, extensive 
experimental evidence suggests that all conics are irreducible whenever 
their number is large enough.

Conjecture. There exists a bound N∗_2n(2)<N_2n(2) such that, whenever a 
smooth 2n-polarized K3-surface X has more than N∗_2n(2) conics, it has 
no lines and, in particular, all conics on X are irreducible.

We know that 249≤N∗_6(2)≤260 is indeed well defined, and it seems 
feasible that N∗_2(2)≥8100 and N∗_4(2)≥720 are also defined; 
furthermore, conjecturally, the lower bounds above are the exact values.

*Date:26 November 2021*, Friday
*Time: 15:40*
*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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