An infinitesimal-birational duality through differential operators

非合冲三次四维簇的Fourier-Mukai伙伴与Gale对偶

Fourier-Mukai partners of non-syzygetic cubic fourfolds and Gale duality

本文研究非合冲三次四维簇，证明其恰有一个非平凡Fourier-Mukai伙伴，利用Gale对偶关联该伙伴，还构造相关反例探讨双有理性猜想。

李代数胚与无穷小叶状结构之间的对偶性

A duality between Lie algebroids and infinitesimal foliations

本文在导出代数几何中，通过利用完备化霍奇滤链精细化PD科斯祖尔对偶，在有限性条件下建立了划分李代数胚与无穷小导出叶状结构之间的等价性。

Brill-Noether duality for moduli spaces of sheaves on K3 surfaces

Components of the Moduli space of sheaves on a K3 surface are parametrized by a lattice; the (algebraic) Mukai lattice. Isometries of the Mukai lattice often lift to symplectic birational isomorphisms of the collection of components. An example of such a birational isomorphism is the Abel-Jacobi map relating the Hilbert scheme of g points on a K3 of degree 2g-2 to an integrable system: the union of Jacobians of hyperplane sections (curves) of genus g. The main results are: 1) We construct a stratified version of a Mukai elementary transformation modeled after dual pairs of Springer resolutions…

Blowups, Gale duality, and moduli spaces

Blowups, Gale duality, and moduli spaces

本文通过Gale对偶将一般位置n+4个点的射影空间Pn的爆破与曲面上秩2向量丛的Gieseker模空间联系起来，并研究极化变化导致的模空间变化，从而部分描述X的双有理几何。

Ringel duality as an instance of Koszul duality

In their previous work, S. Koenig, S. Ovsienko and the second author showed that every quasi-hereditary algebra is Morita equivalent to the right algebra, i.e. the opposite algebra of the left dual, of a coring. Let $A$ be an associative algebra and $V$ an $A$-coring whose right algebra $R$ is quasi-hereditary. In this paper, we give a combinatorial description of an associative algebra $B$ and a $B$-coring $W$ whose right algebra is the Ringel dual of $R$. We apply our results in small examples to obtain restrictions on the $A_\infty$-structure of the $\textrm{Ext}$-algebra of standard module…

Grothendieck duality and Q-Gorenstein morphisms

The notions of $\mathbb Q$-Gorenstein scheme and of $\mathbb Q$-Gorenstein morphism are introduced for locally Noetherian schemes by dualizing complexes and (relative) canonical sheaves. These cover all the previously known notions of $\mathbb Q$-Gorenstein algebraic variety and of $\mathbb Q$-Gorenstein deformation satisfying Kollár condition, over a field. By studies on relative $\mathbf S_{2}$-condition and base change properties, valuable results are proved for $\mathbb Q$-Gorenstein morphisms, which include infinitesimal criterion, valuative criterion, $\mathbb Q$-Gorenstein refinement, a…