Algebraic
Geometry Seminar
Department of Mathematics
Johns Hopkins University
Fall 2019
Regular
meeting time: Tuesdays 4:30-5:30 (Tea served at 4:00)
Place: Gilman 77
|
Date |
Speaker |
Title and Abstract |
|
September 10 |
Joaquin Moraga Princeton University |
Termination of pseudo-effective 4-fold flips Abstract: In this talk, we will discuss relations between
Hermitian metrics and termination of flips for pseudo-effective complex
pairs. In particular, it is expected that ACC for lct's of Hermitian metrics implies termination of flips for pseudo-effective complex pairs in arbitrary dimension. We prove that provided the existence of minimal models, the above invariant can be recovered using generalized log canonical thresholds. Finally, we will sketch the termination of pseudo-effective 4-fold flips using this approach. |
|
September 17 |
Jingjun Han Johns Hopkins University |
Boundedness of ($\epsilon,
n$)-Complements for Surfaces Abstract: I will introduce a reformulation of
a conjecture due to Shokurov on the Boundedness of ($\epsilon,
n$)-Complements. I will show some applications of this conjecture, and give a
sketch of the proof of the conjecture for surfaces. This is an ongoing work
with Guodu Chen. |
|
September 24 |
Nikolaos Tsakanikas Universität des Saarlandes |
Minimal Models
and Weak Zariski Decompositions Abstract: In this talk I will sketch the proof of a reduction
result concerning minimal models, namely that the existence of minimal models
for smooth varieties implies the existence of minimal models for log
canonical pairs. Additionally, I will present some immediate corollaries |
|
October 1 |
Yoshinori Gongyo |
On rationality
theorem for cone of movable in codimension l curves Abstract: We discuss the analogy of rationality, cone, and
contraction theorem for movable in codimension l curves. Our purpose is
to understand it by the language of Minimal model program. This is a joint
work with Sun Rak Choi. |
|
October 8 |
Jaroslaw Wlodarczyk
Purdue
University |
Resolution
via weighted blow-ups Abstract: We provide a simple procedure for resolving,
in characteristic 0, singularities of a variety X embedded in a smooth
variety Y by repeatedly blowing up the worst singularities, in the sense of
stack-theoretic weighted blowings up. This is a joint result with Abramovich
and Temkin. Similar result was discovered independently by McQuillan. We also review some other recent results on desingularization. |
|
October 15 |
Junliang Shen M.I.T |
A tale of two
Lagrangian fibrations Abstract: Lagrangian fibrations, which are higher dimensional
analogs of elliptic K3 surfaces, play a crucial role in the study of
holomorphic symplectic geometry. We will discuss two Lagrangian
fibrations of different flavors. The first is a Lagrangian fibration of a compact holomorphic
symplectic manifold, and the second is Hitchin's integrable system. We will
focus on the interactions between them as well as connections to Hodge
theory, which lead to progress on the P=W conjecture. Based on
joint work with Andrew Harder, Zhiyuan Li, and Qizheng Yin for
the compact case, and joint work with Mark de Cataldo, and
Davesh Maulik for the Hitchin case. |
|
October 22 |
Karl Schwede University of Utah |
Inversion
of adjunction for a mixed characteristic version of multiplier and adjoint
ideals Abstract: Suppose
D is a prime divisor in a normal scheme X. Inversion of adjunction for log
terminal singularities says that the pair (X, D) is purely log terminal (PLT)
if and only if (D, diff) is Kawamata log terminal (KLT), where diff, or
Shokurov's different, can be viewed as a correction term. Takagi proved a
version of this result for F-regular singularities in characteristic. In this
talk, I will discuss joint work with Ma, Tucker, Waldron and Witaszek which
generalizes these results to mixed characteristic schemes via perfectoid big
Cohen-Macaulay (BCM) algebras. As an application, we obtain better understanding of mixed
characteristic perfectoid BCM test ideals as well as an improved
Briancon-Skoda formula in singular mixed characteristic rings. |
|
October 29 |
Gabriele Di
Cerbo Princeton University |
Birational
boundedness of elliptic Calabi-Yau manifolds Abstract: The minimal model program predicts that, up to a
special class of birational equivalences, each projective variety decomposes
into iterated fibrations with general fibers of 3 basic types: Fano
varieties, Calabi-Yau varieties, and varieties of general type. Our
understanding of the boundedness of Fano varieties and varieties of general
type is quite solid but Calabi-Yau varieties are still elusive. In this talk,
I will discuss recent results on the birational boundedness of elliptic
Calabi-Yau varieties with a section. As a consequence, we obtain that there are finitely many possibilities for the Hodge diamond of such varieties. This is joint work with Caucher Birkar and Roberto Svaldi. |
|
November 5 |
Lu Qi M.I.T. |
Boundedness of complements
and local volumes of singularities Abstract: We introduce some applications of the theory of complements in the study of the normalized volume function, based on the recent work of Chenyang Xu and an ongoing joint work with Jingjun Han and Yuchen Liu. |
|
November 12 |
Dan Abramovich Brown University |
|
|
November 19 |
Jianshi Yan Fudan University |
On projective 4-folds of general type with geometric
genus greater than 1 Abstract: We show that for nonsingular projective 4-folds V of general type with geometric genus $p_g>1$, $\varphi_{33}$ is birational onto the image and the canonical volume Vol(V) has the lower bound $\frac{1}{620}$. This is a joint work with Meng Chen. |
|
December 3 |
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