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<div align="center"><big><b><big>Welcome to the 2023 Fall
talks of ODTU-Bilkent Algebraic Geometry Seminars</big></b></big><b><br>
</b></div>
<div align="center"><i>since 2000</i><br>
</div>
<div align="center"><b><b>=================================================================</b></b><br>
<br>
This week the <a
href="http://www.bilkent.edu.tr/~sertoz/agseminar.htm"
target="_blank" moz-do-not-send="true">ODTU-Bilkent
Algebraic Geometry Seminar</a> is <b>online</b><br>
<br>
<i><font color="#ff00ff">This talk will begin at <u><b>15:40</b></u><u> (GMT+3)</u></font></i><br>
<a
href="https://www.timeanddate.com/worldclock/fixedtime.html?msg=ODT%C3%9C-Bilkent+Algebraic+Geometry+Seminar&iso=20231215T1540&p1=19&ah=1"
target="_blank" moz-do-not-send="true">Please check
your time difference between Ankara and your city here</a><br>
<b>=================================================================</b></div>
<div align="center">
<div align="center"><img
src="cid:part1.xH3chPsI.MEYTsij0@bilkent.edu.tr"
alt="" class="" width="529" height="625"></div>
<div align="center"><b><br>
</b><i>Johannes Vermeer (1632-1675)<br>
Girl with a pearl earring (1665)</i><br>
</div>
<div align="left"><b><b><font color="#ff0000">Speaker:</font>
<a href="http://www.fen.bilkent.edu.tr/%7Edegt/"
moz-do-not-send="true">Alexander Degtyarev</a><font
color="#ff0000"><font color="#000000"> <br>
</font></font></b></b><b><b><font
color="#ff0000">Affiliation: </font><i>Bilkent</i></b></b><b><b><font
color="#ff0000"><br>
Title:<font color="#000000"> Lines on singular
quartic surfaces via Vinberg<br>
<br>
</font></font></b></b><b><b><font
color="#ff0000"><br>
</font></b></b></div>
</div>
<div align="left"><b><b><font color="#ff0000">Abstract: </font>Large
configurations of lines (or, more generally,
rational curves of low degree) on algebraic
surfaces appear in various contexts, but only in
the case of cubic surfaces the picture is complete.
Our principal goal is the classification of large
configurations of lines on quasi-polarized
K3-surfaces <i>in the presence of singularities</i>.
To the best of our knowledge, no attempt has been
made to attack this problem from the
lattice-theoretical, based on the global Torelli
theorem, point of view; some partial results were
obtained by various authors using ``classical''
algebraic geometry, but very little is known. The
difficulty is that, given a polarized
N\'eron--Severi lattice, computing the classes of
smooth rational curves depends on the choice of a
Weyl chamber of a certain root lattice, which is not
unique.<br>
<br>
We show that this ambiguity disappears and the
algorithm becomes deterministic provided that <i>sufficiently
many classes of lines are fixed</i>. Based on this
fact, Vinberg's algorithm, and a combinatorial
version of elliptic pencils, we develop an algorithm
that, in principle, would list all extended Fano
graphs. After testing it on octic K3-surfaces, we
turn to the most classical case of simple quartics
where, prior to our work, only an upper bound of 64
lines (Veniani, same as in the smooth case) and an
example of 52 lines (the speaker) were known. We
show that, <i>in the presence of singularities</i>,
the sharp upper bound is indeed 52, substantiating
the long standing conjecture (by the speaker) that
the upper bound is reduced by the presence of smooth
rational curves of lower degree.<br>
<br>
We also extend the classification (I. Itenberg, A.S.
Sertöz, and the speaker) of large configurations of
lines on <i>smooth</i> quartics down to 49 lines.
Remarkably, most of these configurations were known
before.<br>
<br>
This project was conceived and partially completed
during our joint stay at the Max-Planck-Institut
f\ür Mathematik, Bonn. The speaker is partially
supported by TÜBİTAK project 123F111.<font
color="#ff0000"><font color="#000000"><br>
</font></font></b></b></div>
<div align="left"><font color="#ff0000"><font
color="#000000"> <br>
</font></font></div>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000">Date:<font
color="#000000"> 15 December 2023</font></font></b>,
<b>Friday</b></font></font><br>
</div>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000">Time: </font>15:40 <i>(GMT+3)</i></b><br>
<b><font color="#ff0000">Place: </font></b><font
color="#ff0000"><font color="#000000"><b>Zoom</b></font></font></font></font></div>
<blockquote>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><b
style="color:rgb(51,51,51);font-family:arial,verdana,sans-serif;font-size:14px">One
day before the seminar, an announcement
with the Zoom meeting link will be sent to
those who registered with Sertöz.<br>
</b></b></font></font></font></font></p>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><b
style="color:rgb(51,51,51);font-family:arial,verdana,sans-serif;font-size:14px">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.<br>
</b></b></font></font></font></font></p>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><b
style="color:rgb(51,51,51);font-family:arial,verdana,sans-serif;font-size:14px">If
you have not registered before, please
contact him at <a
href="mailto:sertoz@bilkent.edu.tr?subject=Zoom%20Seminar%20Address%20Request"
target="_blank" moz-do-not-send="true">sertoz@bilkent.edu.tr</a>.</b></b></font></font></font></font></p>
</blockquote>
<div align="left"><br>
</div>
<div align="left">You are most cordially invited to
attend.</div>
<div align="left"><br>
</div>
<div align="left">Ali Sinan Sertöz</div>
<div align="left"><font size="1"><i>(PS: To unsubscribe
from this list please send me a note.)</i></font> </div>
<hr>
<pre cols="72">----------------------------------------------------------------------------
Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
Fax: (90)-(312) - 290 1797
e-mail: <a href="mailto:sertoz@bilkent.edu.tr" target="_blank"
class="gmail-moz-txt-link-freetext moz-txt-link-freetext"
moz-do-not-send="true">sertoz@bilkent.edu.tr</a>
Web: <a href="http://sertoz.bilkent.edu.tr" target="_blank"
moz-do-not-send="true">sertoz.bilkent.edu.tr</a>
----------------------------------------------------------------------------</pre>
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