Titles and Short Summaries of the Talks

10 Algebra
9:00–12:00
Algebra
March 20th (Wed) Conference Room I
Final: 2013/2/7
1 Tomohiro Iwami
∗ On certain criterion (weak form) for semistability of 3-fold log flips
(Kyushu Sangyo Univ.) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We will try to give certain criterion, but which is still a weak form, for semistability of 3-
fold log flips appearing in the reduction steps in the proof of 3-fold log flips given by V. V. Shokurov,
under some kinds of characterizations of modified division algorithm by S. Mori for such types of
3-fold log flips.
2 Ryo Akiyama (Shizuoka Univ.) ♯ Classification of quantum affine planes · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Let A be a 3-dimensional quadratic AS-regular algebra with a normal element u ∈ A1.
In this talk, we define a quantum affine plane by a noncommutative affine scheme associated to
A[u −1 ]0, and classify certain quantum affine planes.
3 Yoshifumi Tsuchimoto (Kochi Univ.) ♯ Auslander regularity of non commutative projective space · · · · · · · · · · · 15
Summary: We discuss the Auslander regularity of non commutative projective space over a field
of positive characteristic.
4 Shinya Kitagawa
∗ On certain pencils of plane curves of degree thirteen with a quintuple
(Gifu Nat. Coll. of Tech.) point and nine quadruple points · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: Any genus two fibration on rational surface with Picard number eleven can be
considered as a pencil of plane curves of degree thirteen with a quintuple point and nine quadruple
points through a birational morphism. We consider the case where the fibrations have three singular
fibres of types (V) in the sense of Horikawa, and write down the defining equations of the pencils
with three parameters.
5 Sachiko Saito (Hokkaido Univ. of Edu.) ♯ Real 2-elementary K3 surfaces of type (3,1,1) and degenerations · · · · · 10
Summary: We consider real 2-elementary K3 surfaces (X, τ, φ) of type ((3, 1, 1), −1). The fixed
point (anti-bi-canonical) curve A of τ is the disjoint union of a nonsingular rational curve A0 and
a nonsingular curve A1 of genus 9. X has an elliptic fibration with its section A0 and a unique
reducible fiber E + F , where F might be reducible. Contracting the curve F on the quotient surface
X/τ, we get the real 4-th Hirzebruch surface F4. The image A ′ 1 of A1 on F4 has one real double
point. We try to classify the isotopy types of the real parts RA ′ 1 of A ′ 1 on RF4. We enumerate up
all the isometry classes of involutions of the K3 lattices of type ((3, 1, 1), −1), and consider their
correspondences to the “non-increasing simplest degenerations” of real nonsingular anti-bi-canonical
curves on RF4.