Giancarlo Urzua (Pontificia Universidad Catolica de Chile)
Giancarlo Urzua Visitor (2024.11.8-2024.11.13) from Pontificia Universidad Catolica de Chile Office: -
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Giancarlo Urzua, The Birational Geometry of Markov Numbers
B236-1 IBS, Korea, Republic ofSpeaker Giancarlo Urzua Pontificia Universidad Catolica de Chile The projective plane is rigid. However, it may degenerate to surfaces with quotient singularities. After the work of Bădescu and Manetti, Hacking and Prokhorov 2010 classified these degenerations completely. They are Q-Gorenstein partial smoothings of P(a2, b2, c2), where a, b, c satisfy the Markov …
Izzet Coskun, The Geometry of Moduli Spaces of Sheaves on P2
B236-1 IBS, Korea, Republic ofSpeaker Izzet Coskun University of Illinois Chicago In this talk, I will explain how to use Bridgeland stability conditions to compute the ample and effective cones of moduli spaces of sheaves on the projective plane. I will describe the birational geometry of these moduli spaces and give applications to the higher rank interpolation …
Izzet Coskun, The Higher Rank Brill-Noether Problem on Surfaces
B236-1 IBS, Korea, Republic ofSpeaker Izzet Coskun University of Illinois Chicago In this talk, I will explain how to use Bridgeland stability conditions to compute the cohomology of a general stable sheaf on a K3 or abelian surface. This talk is based on joint work with Howard Nuer and Kota Yoshioka.
Luca Schaffler, An Explicit Wall Crossing for the Moduli Space of Hyperplane Arrangements
B236-1 IBS, Korea, Republic ofSpeaker Luca Schaffler Roma Tre University The moduli space of hyperplanes in projective space has a family of geometric and modular compactifications that parametrize stable hyperplane arrangements with respect to a weight vector. Among these, there is a toric compactification that generalizes the Losev-Manin moduli space of points on the line. We study …
Yen-An Chen, Toric Fano Foliations
B236-1 IBS, Korea, Republic ofSpeaker Yen-An Chen National Taiwan University In recent years, there are significant developments of the minimal model program for foliated varieties. It is intriguing to ask if Fano foliations form a bounded family. It is anticipated that Borisov-Alexeev-Borisov conjecture also holds in the context of foliations. In this talk, I will discuss the …
Luca Schaffler, Unimodal Singularities and Boundary Divisors in the KSBA Moduli of a Class of Horikawa Surfaces
B236-1 IBS, Korea, Republic ofSpeaker Luca Schaffler Roma Tre University Smooth minimal surfaces of general type with K2=1, pg=2, and q=0 constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli space M of their canonical models admits a modular compactification M via the minimal model program. We describe eight new irreducible boundary …
Sungmin Yoo, Convergence of Sequences of the Bergman Type Volume Forms
B236-1 IBS, Korea, Republic ofSpeaker Sungmin Yoo Incheon National University Following the Yau-Tian-Donaldson conjecture, the construction of sequences of Bergman-type metrics converging to a canonical metric on a polarized manifold has been studied by many mathematicians including Tian, Donaldson, Tsuji, Berman, Berndtsson, and others. In this talk, I will introduce my recent findings on the uniform convergence …
Yonghwa Cho, Double Point Divisors from Projections
B236-1 IBS, Korea, Republic ofSpeaker Yonghwa Cho Gyeongsang National University Consider a smooth projective variety of codimension e. A general projection from a linear subspace of dimension (e-2) is birational, hence the non-isomorphic locus forms a proper closed subset of X. Mumford showed that this non-isomorphic locus is not merely a closed subset, but is naturally endowed …
Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program I
B236-1 IBS, Korea, Republic ofSpeaker Sung Wook Jang IBS CCG Minimal model program (abbreviated as MMP) is a central problem in birational geometry. The MMP is a sequence of divisorial contractions or flips, which makes the canonical divisor closer to a nef divisor. If the MMP successfully terminates, then we have either a minimal model or a …
Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program II
B236-1 IBS, Korea, Republic ofSpeaker Sung Wook Jang IBS CCG We are interested in an anticanonical divisor and hope to establish the MMP for an anticanonical divisor. We believe that the beginning point is the potential log discrepancy that controls singularities of a possible resulting model of MMP for an anticanonical divisor. In this talk, we will …
Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program III
B236-1 IBS, Korea, Republic ofSpeaker Sung Wook Jang IBS CCG We can run an MMP for an lc pair. However, in general, we do not know whether the MMP terminates or not. Nevertheless, we can show that special MMP terminates. Immediately, we can prove the existence of minimal models for certain pairs. Analogously, for an anticanonical divisor, …