[Turkmath:5229] ODTU-Bilkent Algebraic Geometry Seminar-Zoom-493

[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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*image.png *//
/Paul Gauguin (1848-1903)
/

**Speaker:Sergey Finashin
**
**Affiliation: ODTÜ
Title:Two kinds of real lines on real del Pezzo surfaces and invariance 
of their signed count

**
**Abstract:**In his classical treatise on real cubic surfaces, Segre 
discovered two kinds of real lines which he called elliptic and hyperbolic.

His enumeration indicated that the number of hyperbolic is greater by 3 
than the number of elliptic ones independently of a real structure on 
the cubic surface.

However this property did not receive a conceptual explanation until 
recently: in a joint work with V.Kharlamov we interpreted a signed count 
of lines as a signed count of zeroes of some vector field in a 
Grassmannian (and so, it is Euler’s number of the corresponding vector 
bundle).

In the current work that I will present, we develop an alternative 
approach to counting lines on real del Pezzo surfaces X of degrees 1 and 
2 (a projective plane blown up at 8 or 7 generic points, respectively).  
The two types of real lines are distinguished by certain canonical 
Pin-structure on the real locus X_R (this looks different from the 
approach of Segre, but is equivalent to it in the case of cubic surfaces).

A signed count of real lines is interpreted as some lattice root 
enumeration, which lets us prove our invariance properties for del Pezzo 
of degree 1 and 2, like in the case of cubic surfaces.

*Date:5 November 2021*, 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
Web: sertoz.bilkent.edu.tr <http://sertoz.bilkent.edu.tr>
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