IPM Algebraic Geometry Seminar
IPM is holding a biweekly zoom Algebraic Geometry seminar for Winter/Spring 2024.
Where: Zoom
Meeting ID: 908 611 6889
Passcode: 13440 × the number of lines on a cubic surface
Seminar mailing list: google group
Poster: here
Past Seminar Series
Upcoming Talks
Speaker: Razieh Ahmadian, Shahid Beheshti University (Iran)
Title: Hironaka's Question F and its Simplification
Abstract: A special case of Hironaka's QUESTION F, named F', asks about the strong
factorization of birational maps between reduced nonsingular algebraic schemes, which is still open. Suppose
that $\varphi : X\dashrightarrow Y$ is such a map, and let $U\subset X$ be the open subset where $\varphi$ is an isomorphism. This problem asks if there exists a diagram
$$
\xymatrix{ & Z \ar[dl]_{\varphi_{1}}\ar[dr]^{\varphi_{2}}\\
X \ar[rr]^{\varphi} & & Y}
$$
where the morphisms $\varphi_{1}$ and $\varphi_{2}$ are sequences of blow-ups of non-singular centers disjoint
from $U$. In this talk, we will discuss how strong factorization can be simplified by providing a complete answer to
the problem of toroidalization of morphisms, while we introduce the strong Oda conjecture.
Date: May 1, 2024
Time: 17:30-19:00 Tehran time
Speaker: Rita Pardini, University of Pisa (Italy)
Title: Exploring the boundary of the moduli space of stable surfaces: some explicit examples
Abstract: I will briefly recall the notion of stable surfaces and of the corresponding moduli space. Then I will outline a
partial description of the boundary points in the case of surfaces with $K^2=1$, $p_g=2$ (joint work with Stephen Coughlan, Marco Franciosi,
Julie Rana and Soenke Rollenske, in various combinations) and, time permitting, in the case of Campedelli and Burniat surfaces (joint work with Valery Alexeev).
Date: May 15, 2024
Time: 17:30-19:00 Tehran time
Speaker: Jonas Stelzig, LMU Munich (Germany)
Title: Linear combinations of cohomological invariants of compact complex manifolds
Abstract: In the 50s, Hirzebruch asked which linear combinations of Hodge and
Chern numbers are topological invariants of compact complex manifolds.
Building on ideas of Schreieder and Kotschick, who solved the Kähler
case, I will present a general answer to this question (and some related
ones). Furthermore, I will outline a program how to tackle similar
questions when incorporating more cohomological invariants, eg the
dimensions of the Bott Chern cohomology groups. This will naturally lead
to an algebraic study of the structure of bicomplexes, as well as a
number of challenging geometric construction problems.
Date: May 29, 2024
Time: 17:30-19:00 Tehran time
Speaker: Emilia Mezzetti, University of Trieste (Italy)
Title: Hilbert functions, Lefschetz properties and Perazzo hypersurfaces
Abstract: TBA
Date: June 12, 2024
Time: 17:30-19:00 Tehran time