미야오카 등식을 만족하는 극소 사영 다양체의 구조 정리
본 논문에서는 미야오카 등식을 만족하는 극소 사영 klt 다양체의 표준 divisor가 semi-ample하며, 이러한 다양체는 유한 준-´etale 덮개를 취하면 부드러워지고 그 구조가 명확하게 기술됨을 보입니다.
擬線性熱帶緊化
擬線性熱帶緊化是對經典熱帶緊化概念的推廣，它保留了超平面排列補集緊化的許多良好性質，例如schon性質和Chow環的簡單描述。
준선형 열대 컴팩트화
본 논문은 초평면 배열의 여집합의 컴팩트화가 가지는 바람직한 속성들을 만족하는, 준선형(quasi-linear) 열대 컴팩트화라는 더 광범위한 종류의 열대 컴팩트화를 소개하고, 준선형 컴팩트화가 schön임을 보이고, 그 교차 이론이 대응하는 열대 팬의 교차 이론에 의해 완전히 설명됨을 보여줍니다.
準線形熱帯コンパクト化とその応用
超平面配置の補集合のコンパクト化として知られる熱帯コンパクト化の概念を拡張し、準線形熱帯コンパクト化を導入する。準線形熱帯コンパクト化は、超平面配置のコンパクト化と同様に、多くの優れた幾何学的性質を備えていることを示す。特に、準線形コンパクト化は常に Schoen であり、その交叉理論は対応する熱帯ファンの交叉理論によって完全に記述される。
Quasilinear Tropical Compactifications: Extending the Geometry of Hyperplane Arrangement Compactifications
This paper introduces the concept of "quasilinear tropical compactifications," a class of compactifications of subvarieties of algebraic tori that share desirable properties with compactifications of hyperplane arrangement complements, such as being "schön" and having a Chow ring determined by the tropical fan.
A Tangent Category Perspective on Connections in Algebraic Geometry: Exploring the Relationship Between Abstract and Classical Notions of Connections
This paper demonstrates that the abstract notion of a connection in tangent categories, when applied to the tangent category of affine schemes, aligns with the classical algebraic geometry definition of a connection on a module.
通過 $\mathbb{C}^*$ 作用刻劃有理齊性空間
本文證明了具有 Picard 數為一且帶有特定有理曲線族的平滑代數簇，若允許一個滿足特定條件的 $\mathbb{C}^*$ 作用，則該代數簇必為不可約的 Hermitian 對稱空間。
$\mathbb{C}^*$-作用による有理等質空間の特徴付け
ピカール数が1で、特別な支配的な有理曲線族と均等化された $\mathbb{C}^*$-作用を許容する滑らかな多様体は、孤立した極値固定点を持つ場合に限り、既約エルミート対称空間である。
Rational Normal Curves, Chip Firing, and Free Resolutions: A Combinatorial Approach
This paper introduces a novel combinatorial approach to studying rational normal curves by connecting them to the chip firing game and parcycles, leading to explicit constructions of minimal free resolutions for their ideals and Gr"obner degenerations.
Residual Intersections of Opposite Schubert Varieties Defined by a Pattern in ADE Types
This mathematics research paper presents a pattern for defining opposite Schubert varieties in ADE types, where specific pairs of these varieties, called Ulrich pairs, exhibit a residual intersection property. This property reveals that the defining ideal of one variety in the pair can be obtained by taking the residual intersection of the other variety with a specific sequence of Plücker coordinates.
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