김순영(서강대)

제목 The cyclic group scheme of order p and Godeaux surfaces

초록 Over an algebraically closed field of characteristic p, there are 3 group schemes Z_p, μ_p and α_p. The Tate-Oort group scheme G_p puts these together in one family in characteristic zero. We study some constructions related to G_p and apply it to give a uniform construction of the Godeaux surfaces with Pic^τ of order 5. This is joint work in progress with Miles Reid.

김호성(KIAS)

제목 Curvilinear Hilbert scheme

초록 In this talk I will introduce the definition of Curvilinear Hilbert scheme and descibe its singularities.

This result enables us to understand a minimal rational component of a Fano threefold. This is a joint work with Hwayoung Lee.

이광우(GIST)

제목 Automorphism groups of some K3 surfaces and their Hilbert schemes

초록 We compute automorphism groups of K3 surfaces with a given intersection matrix of Neron-Severi lattice of rank 2. This construction of K3 surface was inspired by Prof. Oguiso. Moreover, we determine the automorphism groups of Hilbert schemes of such K3 surfaces.

이철규(KIAS)

제목 On worst unstable zero-dimensional schemes and their properties

초록 In this talk, we will compute an explicit equation of a zero-dimensional projective scheme represented by an arbitrary worst unstable point of a Hilbert scheme for all but finitely many choices of Plucker coordinate.

We will show that such schemes are geometrically bad; it has a unique closed point and is not K-stable.

정기룡(경북대)

제목 Gopakumar-Vafa invariants on CY 4-fold

초록 During the last several decades, the enumerative geometry on CY-threefold has been studied in a group of mathematician and theoretic physicists. As a generalization of this one, interests of researcher moves into the case of the CY-fourfold. In this talk, by following the work of Cao, Maulik, and Toda relating with GV-type invarint on CY-fourfold, we count the rational curves on open CY 4-folds (for example, the total space of the canonical line bundle of the Fano threefold of index two and the rank two vector bundles over the projective plane). This is a work on progress with Jinwon Choi and Han-Bom Moon.

정승조(KIAS)

제목 Cubic fourfolds and Fano schemes of lines

초록 Let X be a smooth cubic fourfold with a group G action. Suppose that the group action induces a symplectic action on the Fano scheme F(X) of lines on X. In the case where the quotient F(X)/G has a symplectic resolution Y, I present a possible moduli description of Y in terms of Bridgeland stability on the equivariant Kuznetsov category of X. This is based on joint work in progress with Genki Ouchi.