Meeting room 2 (room 1 only morning of 16th), Yuzawa-cho Kouminkan, 2822 Oza Yuzawa, Yuzawa-cho, Uonuma-gun, Niigata, 949-6101, Japan
[Link]
13th
Yusuke Nakamura
TBA
Chen Jiang
Remarks on Kawamata's effective non-vanishing conjecture
Abstract:Kawamata proposed a conjecture concerning when a nef divisor has global sections. In particular, this conjecture predicts that, every ample line bundle on a Calabi-Yau manifold has a non-trivial global section. I will show that this conjecture holds for any hyperkahler manifolds of dimension 6, base on a joint work with Yalong Cao.
14th
Kenta Sato
General hyperplane sections of 3-folds in positive characteristic
Abstract:Since the Bertini theorem fails in positive characteristic,
it is not clear whether a general hyperplane section of a klt 3-fold in positive characteristic has only klt singularities or not.
We give an affirmative answer when the characteristic is larger than 5.
This talk is based on joint work with Shunsuke Takagi.
Akiyoshi Sannai
Abelian varieties in positive characteristic
Abstract:We give a characterization of ordinary abelian varieties by using the
Frobenius push forward of the structure sheaf; a smooth projective variety
X is ordinary abelian variety
if and only if (1) K_X is pseudo effective (2) If the characteristic of
the base field is bigger than 2, F_*O_X split into direct sum of line
bundles, In characteristic 2, F_*^2O_X has the same property above.
Yoshinori Gongyo
Note on extremal rays on the cone of movable curves
Abstract: We discuss the cone theorem which is conjectured by Batyrev.
Taro Sano
Deformations of VNC Calabi-Yau varieties
Abstract:Given a 1-parameter degeneration of a Calabi-Yau manifold,
we can obtain some topological information of the original Calabi-Yau
manifold from the degenerate fiber.
We can sometimes construct such a family by deforming a singular variety.
Kawamata--Namikawa proved that a certain normal crossing variety with
trivial dualizing sheaf has a smoothing.
In this talk, I will talk about a generalization of this result to
V-normal crossing varieties.
15th Free discussion
16th
Atsushi Ito
On derived equivalence and Grothendieck ring of varieties
Abstract:I will talk about a relation in the Grothendieck ring between the classes of derived equivalent varieties.
This is a joint work with Makoto Miura, Shinnosuke Okawa, and Kazushi Ueda.
Katsuhisa Furukawa
Dimension of the space of conics on Fano hypersurfaces
Abstract:R. Beheshti showed that, for a smooth Fano hypersurface $X$ of degree $\leq 8$ over the complex number field $\CC$, the dimension of the space of lines lying in $X$ is equal to the expected dimension.
We study the space of coincs on $X$. In this case, if $X$ contains some linear subvariety, then the dimension of the space can be larger than the expected dimension.
In this paper, we show that, for a smooth Fano hypersurface $X$ of degree $¥leq 6$ over $\CC$, and for an irreducible component $R$ of the space of coincs lying in $X$, if the $2$-plane spanned by a general conic of $R$ is not contained in $X$, then the dimension of $R$ is equal to the expected dimension.
Takehiko Yasuda
A refinement of the motivic Serre invariant
Abstract:In this talk, I will talk about a certain refinement of the motivic Serre invariant defined by Loeser and Sebag. In 60's, Serre classified compact analytic manifolds over a local field and showed that they are completely classified by an invariant belonging to Z/(q-1)Z with q the cardinality of the residue field. As an analogue of this, the motivic Serre invariant was defined for rigid varieties as elements of the Grothendieck ring of varieties modulo L-1. The main result in this talk is that in some less general situation, if we assume the desingularization and weak factorization conjectures, then the invariants lift to modulo the square of L-1.
Yujiro Kawamata
A remark on a theorem of Fujita
Abstract:
Let $f: X \to Y$ be a surjective morphism from a compact K\"ahler manifold to a projective manifold
whose fibers are connected.
Assume that there are normal crossing divisors $B$ and $C$ on $X$ and $Y$, respectively,
such that $B = f^{-1}(C)$ set-theoretically and such that $f$ is smooth on $X \setminus B$.
Then a semi-positivity theorem states that
$V = f_*\mathcal{O}_X(K_X+B-f^*(K_Y+C))$ is a locally free sheaf which is numerically semi-positive.
A theorem of Fujita says that, if $\dim Y = 1$, then there is a decomposition $V = W \oplus U$,
where $W$ is an ample vector bundle and $U$ has a unitary flat connection.
A result by Catanese and Dettweiler states that there are many examples
where $U$ is not semi-ample.
I will explain these results and a generalization to the case where $\dim Y$ is arbitrary.
This is a joint work with Fabrizio Catanese.
17th
Keiji Oguiso,
Higher dimensional projective manifolds with primitive automorphisms of
positive entropy
Abstract:
We show that, in any dimension greater than one, there are an abelian
variety, a smooth rational variety and a Calabi-Yau manifold, with
primitive birational automorphisms of first dynamical degree $>1$. We
also show that there are smooth complex projective Calabi-Yau manifolds
and smooth rational manifolds, of any even dimension, with primitive
biregular automorphisms of positive topological entropy.
Chenyang Xu,
Moduli space of smoothable K-semistable Q-Fano varieties
Abstract:It is expected that there is a compact moduli space parametrizing all K-polystable Fano varieties. However, the standard GIT method can't be applied as we know some of them are not GIT-stable. In this talk, we will discuss a construction of a proper algebraic space parametrizing K-polystable smoothable Fano varieties. We rely on the analytic proof of YTD-conjecture. Then we follow a general strategy of showing that an Artin stack has a good moduli space, using a mixture of local and global conditions. We will explain the reasons why the conditions hold in our situation.
