Mini-workshop on algebraic surfacesDate : Oct. 15 - 16 , 2015 Place : 1423 , KIAS |
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Speaker : Miles Reid (Univ. of Warwick / KIAS)
Title : TBA
Speaker : DongSoo Shin (Chungnam National University)
Title: Milnor fibers of complex surface singularities
Abstract: In this series of lectures, I will introduce my recent results on Milnor fibers of complex surface singularities. At first, I provides a complete classification of resolution graphs of normal surface singularities admitting a smoothing whose Milnor fiber is a rational homology disk, which verifies a conjecture of J. Wahl regarding such singularities. At the second lecture, I focus on Milnor fibers of quotient surface singularities. Especially, I give an explicit algorithm to identify Milnor fibers mainly via techniques from the minimal model program for 3-folds. These are joint works with Heesang Park, Jongil Park, Andras Stipsicz, and Giancarlo Urzua.
Speaker : DongSeon Hwang (Ajou University)
Title : Zhang's theory on log del Pezzo surfaces of rank one
Abstract : De-Qi Zhang initiated the systematic study of the classification problem of log del Pezzo surfaces of rank one in his doctoral thesis. It has been developed further by many other mathematicians and has been used to investigate some properties of log del Pezzo surfaces.
In this talk, I will review the development of his theory together with the recent progress. Some part will be discussed in detail together with the proof. If time permit, I will also speak on the classification of log del Pezzo surfaces of rank one using this theory.
Speaker : Yonghwa Cho (KAIST)
Title : Line bundles on Dolgachev surfaces constructed via $mathbb Q$-Gorenstein smoothing
Abstract : In the first part of this talk, I will introduce how to construct Dolgachev surfaces using Lee-Park construction. After then, I give a complete description of Picard group of the Dolgachev surfaces constructed in this way. Main ingredient is the Hacking's idea, which associates an exceptional vector bundle with a degeneration to a Wahl singularity. Finally, I will discuss how can we compare the line bundles on the singular rational surfaces(which appear in Lee-Park construction) and the line bundles on the Dolgachev surfaces. This is a joint work in progress with Yongnam Lee.
Speaker : Kyoung-Seog Lee (KIAS)
Title : Geometry and derived categories of some elliptic surfaces
Abstract : I will review the general theory of geometry and derived categories of elliptic surfaces. Then I will explain geometry of some elliptic surfaces constructed from fake projective planes. Finally I will present numerical exceptional collections of maximal length on these elliptic surfaces. This is joint work in progress with JongHae Keum.