[Turkmath:7450] ODTU-Bilkent Algebraic Geometry Seminar-Zoom-583

[Ali Sinan Sertöz]

*Welcome to the 2026 Spring talks of ODTÜ-Bilkent Algebraic Geometry 
Seminars**
*
/since 2000/
**=================================================================**

This week the ODTÜ-Bilkent Algebraic Geometry Seminar 
<http://www.bilkent.edu.tr/~sertoz/agseminar.htm>  is *online*

/This talk will begin at _*15:40*__ (GMT+3)_/
Please check your time difference between Ankara and your city here 
<https://www.timeanddate.com/worldclock/fixedtime.html?msg=ODT%C3%9C-Bilkent+Algebraic+Geometry+Seminar&iso=20260403T1540&p1=19&ah=1>
*=================================================================

*

/Ben Viegers (1886-1947)
/
/
/
/
/
**Speaker: Roberto Villaflor Loyola 
<https://sites.google.com/view/roberto-villaflor-loyola/home>**
******Affiliation: /Universidad Técnica Federico Santa María

/**
**Title:  On the linear cycles conjecture
**
**Abstract:**  The classical Noether-Lefschetz theorem claims that a 
very general degree d>3 surface in P3 has Picard number one. The locus 
of surfaces with higher Picard rank is known as the Noether-Lefschetz 
locus, which is known to have a countable number of irreducible 
components. For d>4, it is classical result due independently to Green 
and Voisin, that the unique component of highest codimension corresponds 
to the locus of surfaces which contain lines.

The natural generalization of this question to higher dimensional 
hypersurfaces of the projective space is known as the "/linear cycles 
conjecture/", and remains open even for fourfolds. For surfaces, the 
proof is based in the fact that locally (analytically) one can 
parametrize each component by a Hodge locus, and then use the 
Infinitesimal Variation of Hodge Structure to compute (and bound) the 
dimension of its Zariski tangent space. A natural stronger version of 
the linear cycles conjecture is that the Hodge loci with maximal tangent 
space are those corresponding to linear cycles.

In this talk I will report on recent results disproving this conjecture 
for all degrees and dimensions.

This is a joint work with Jorge Duque Franco.
*
*
*Date: 3 April 2026, Friday*
*Time: 15:40 /(GMT+3)/*
*Place: **Zoom*

    /*Participants who have registered will receive the Zoom link via
    email one day before the seminar.*/

    /*If you registered for a previous talk in this series, there's no
    need to register again—you'll automatically receive the link for
    this session.*/

    /*If you haven't registered yet, please contact
    sertoz at bilkent.edu.tr to be added to the mailing list.*/

You are most cordially invited to attend.

Ali Sinan Sertöz

*/*/This seminar series is organized by a joint team from ODTÜ and Bilkent

Alexander Degtyarev (Bilkent)
Ali Sinan Sertöz (Bilkent) contact person
Ali Ulaş Özgür Kişisel (ODTÜ)
Yıldıray Ozan (ODTÜ)
/*/*


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Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
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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