Yong Hu, Noether-Severi Inequality and Equality for Irregular Threefolds of General Type

B266 IBS, Korea, Republic of

     Speaker Yong Hu KIAS For complex smooth irregular 3-folds of general type, I will introduce the optimal Noether-Severi inequality. This answers an open question of Zhi Jiang in dimension three. Moreover, I will also completely describe the canonical models of irregular 3-folds attaining the Noether-Severi equality. This is a joint work with Tong

Sukmoon Huh, Logarithmic Sheaves on Projective Surfaces

B266 IBS, Korea, Republic of

     Speaker Sukmoon Huh Sungkyunkwan University A logarithmic sheaf is a sheaf of differential one-forms on a variety with logarithmic poles along a given divisor. One of the main problems on this object is to see whether Torelli property holds, i.e. whether two different divisors define two non-isomorphic logarithmic sheaves. In this talk, after

Yonghwa Cho, Cohomology of Divisors on Burniat Surfaces

B266 IBS, Korea, Republic of

     Speaker Yonghwa Cho KIAS A (primary) Burniat surface is a complex surface of general type that can be obtained as a bidouble cover of del Pezzo surface with K2 = 6. The Picard group is an abelian group of rank 4 with torsion part isomorphic to (Z/2)6. Alexeev studied the divisors on Burniat

Jinhyung Park, Comparing Numerical Iitaka Dimensions

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     Speaker Jinhyung Park Sogang University There are several definitions of the "numerical" Iitaka dimensions of a pseudoeffective divisor, which are numerical analogues to the Iitaka dimension. Recently, Lesieutre proved that notions of numerical Iitaka dimensions do not coincide. In this talk, we prove that many of numerical Iitaka dimensions are equal to the

Sung Rak Choi, Subadditivity of Okounkov Bodies

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     Speaker Sung Rak Choi Yonsei University We will investigate the subadditivity theorem of Okounkov bodies for algebraic fiber spaces. As an application, we obtain the subadditivity of the numerical Kodaira dimension and the restricted volume for algebraic fiber spaces. As a byproduct, we obtain a criterion of birational isotriviality in terms of Okounkov

Changho Han, Compact Moduli of Lattice Polarized K3 Surfaces with Nonsymplectic Cyclic Action of Order 3

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     Speaker Changho Han University of Georgia Observe that any construction of "meaningful" compactification of moduli spaces of objects involve enlarging the class of objects in consideration. For example, Deligne and Mumford introduced the notion of stable curves in order to compactify the moduli of smooth curves of genus g, and Satake used the

Yoon-Joo Kim, The Dual Lagrangian Fibration of Compact Hyper-Kähler Manifolds

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     Speaker Yoon-Joo Kim Stony Brook University A compact hyper-Kähler manifold is a higher dimensional generalization of a K3 surface. An elliptic fibration of a K3 surface correspondingly generalizes to the so-called Lagrangian fibration of a compact hyper-Kähler manifold. It is known that an elliptic fibration of a K3 surface is always "self-dual" in

Yuchen Liu, K-stability and Moduli of Quartic K3 Surfaces

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     Speaker Yuchen Liu Northwestern University We show that K-moduli spaces of (P3, cS) where S is a quartic surface interpolates between the GIT moduli space and the Baily-Borel compactification as c varies in (0,1). We completely describe the wall crossings of these K-moduli spaces. As a consequence, we verify Laza-O’Grady's prediction on the

Yewon Jeong, Several Types of Dual Defective Cubic Hypersurfaces

TBA

     Speaker Yewon Jeong IBS, Center for Complex Geometry Given a hypersurface X = V(f) in a complex projective space, we say X is dual defective if the Gauss map of X, the restriction of the gradient map of f on X, has positive dimensional fibers. Especially for cubics, there is an interesting classification

Zhi Jiang, On Syzygies of Abelian Varieties

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     Speaker Zhi Jiang SCMS, Fudan University Syzygies of ample line bundles on abelian varieties have attracted lots of attentions in recent years. People tried to study these geometric objects by different methods, including Okounkov bodies, X-methods from MMP, and generic vanishing theory. We will report some progress on this subject based on the

Feng Shao, The Bigness of Tangent Bundles of Projective Manifolds

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     Speaker Feng Shao IBS, Center for Complex Geometry Let X be a Fano manifold. While the properties of the anticanonical divisor -KX and its multiples have been studied by many authors, the positivity of the tangent bundle TX is much more elusive. In this talk, we give a complete characterization of the pseudoeffectivity

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