Titles and Short Summaries of the Talks

12 Algebra
14:15–16:45
Final: 2013/2/7
12 Kazunori Yasutake (Kyushu Univ.) ∗ On Fano fourfolds with nef vector bundle Λ 2 TX · · · · · · · · · · · · · · · · · · · · 10
Summary: Fano variety is a variety with ample anti-canonical line bundle. In 1992, Campana
and Peternell classified threefolds with nef vector bundle Λ 2 TX. I will talk about a classification of
Fano fourfolds whose Picard number is at least two with this property.
13 Kiwamu Watanabe (Saitama Univ.) ∗ Fano 5-folds with nef tangent bundles · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We prove that smooth Fano 5-folds with nef tangent bundles and Picard numbers
greater than one are rational homogeneous manifolds.
14 Ken-ichi Yoshida (Nihon Univ.) ♯ Ulrich ideals and modules on 2-dimensional rational singularities · · · · · 15
Shiro Goto (Meiji Univ.)
Kazuho Ozeki (Yamaguchi Univ.)
Ryo Takahashi (Nagoya Univ.)
Kei-ichi Watanabe (Nihon Univ.)
Summary: We classify all Ulrich ideals and modules on 2-dimensional rational double points.
15 Takayuki Hibi
(Osaka Univ./JST CREST)
Akihiro Higashitani (Osaka Univ.)
♯ Normality of dilated polytopes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: For an integral convex polytope P of dimension d, let µ(P) denote the maximal degree
of the Hilbert basis of the polyhedral cone arising from P. In this talk, it is proved that given an
integer d ≥ 4, there exists an integral convex polytope P of dimension d with µ(P) = d − 1 such
that (d − 2)P is normal. Moreover, given integers d ≥ 3 and 2 ≤ j ≤ d − 1, we show the existence
of an empty simplex of P of dimension d with j = µ(P) such that qP cannot be normal for any
1 ≤ q < j.
16 Akihiro Higashitani (Osaka Univ.) ♯ Non-normal very ample toric rings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In this talk, it is proved that for given integers h and d with h ≥ 1 and d ≥ 3, there
exists a non-normal very ample integral convex polytope of dimension d which has exactly h holes.
17 Kazunori Matsuda (Nagoya Univ.) ∗
Satoshi Murai (Yamaguchi Univ.)
Regularity bounds for binomial edge ideals · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We show that the Castelnuovo–Mumford regularity of the binomial edge ideal of a
graph is bounded below by the length of its longest induced path and bounded above by the number
of its vertices.