Algebraic Geometry Papers of the Week

Using the incidence correspondence between $X$ and $M$, we construct a family $\mathcal E$ of objects in the Kuznetsov component $\operatorname{Ku}(X)$.

Within our cyclic encoding framework, we obtain a stronger upper bound that is approximately $1.28$ times the lower bound achieved by our exponential-time construction.

By introducing the notion of stable compatibility, we provide a framework in the model category theory which addresses the existence of a stable model structure on the category of modules over a monad.

We bound the action of the mapping class group of (X,P) on the rational cohomology groups of the ordered configuration spaces F_n(X-P) of X-P. In particular, we show that, when #P < 2, the diagonal action of the mapping class group on the direct sum of the H^n(F_n(X-P)) is faithful, and determine its kernel when #P > 1.

In this paper, we give a local resolution theorem for log-rank adapted morphisms: after finite sequences of smooth local blow-ups, the first two log-Fitting ideals \mathcal{F}\_{n--1}(\sigma) and \mathcal{F}\_{n--2}(\sigma) become principal monomial ideals.

We construct simple coherent classes and compute their normalized difference operators for the two-node quiver Coulomb branch with gauge group $GL_1\times GL_2$ and $m-1$ framing columns at the second node.

We study the equality case of the inequalities between the Lyapunov spectrum and the Harder--Narasimhan slopes of a semi-simple local system with non-expanding cusp monodromy over a finite-area hyperbolic surface.

We prove that $f_*\mathcal{O}_X(D)$ is globally generated after pullback by an isogeny.

We formulate a canonical quantum curve conjecture $\widehat H\Psi_*=0$ for spectral curves of positive genus.

We give a proof that an isolated algebraic symplectic singularity of dimension $2n\ge 4$ admitting a projective symplectic resolution is analytically isomorphic to the minimal nilpotent orbit closure in $\mathfrak{sl}_{n+1}$ at the origin.

In this paper, we prove Butler's conjectures for $g\ge8$ in the two cases in which the Brill-Noether geometry of a general curve is known, namely rank one and the range $\mu(E)>2g-2$.

We prove the algebraicity of period images in arithmetic quotients without using o-minimality.

We study Hodge--Riemann relations for ordinary, sequential, and weak $m$-positive real $(1,1)$-forms in complex dimension $d$.

We prove that for the one-point evaluation codes $C_i$ of length $N_i=728\cdot27^{\,i-1}$ and pole order $\lfloor N_i/5\rfloor$ on the Garcia--Stichtenoth tower over $\mathbb{F}_{729}$, the triple $(C_i,C_i,C_i)$ has product expansion with a constant independent of $i$.

Let $X\subset\PP^{M-1}$ be a smooth hypersurface of degree $d<M$, and let $\Ku(X)$ be its Kuznetsov component, the orthogonal complement of the line bundles $\OO_X,\dots,\OO_X(M-d-1)$ in the derived category. We prove that $\Ku(X)$ determines $X$ for every smooth quartic in $\PP^{4k+1}$, $k\geq1$; together with earlier work, this gives categorical Torelli for every smooth hypersurface of degree $d<M$ with $d\nmid M$.

We derive an Eynard-Orantin topological recursion for intersection numbers involving Norbury's $\Theta$-class together with $\psi$-classes and higher $\kappa$-classes.

Let $Y$ be a smooth projective complex variety of dimension $n$ with trivial Chow groups, and let $f: X\rightarrow Y$ be a cyclic cover of degree $d$ branched over a smooth ample divisor $D\in |dL|$. We show that a naturally constructed Chow--Künneth decomposition of $X$ is $m$-fold $mn$-multiplicative for each integer $m\geq2$ and that its stable motivic multiplicativity defect satisfies $\mathfrak{sd}(X)\leq 2dn$.

In this paper, we prove that the residual map is a locally trivial topological fibration over each open flat of the stratification induced by the resonance arrangement.

In this article, we use Wu's method to prove Budur's multi-variable $n/d$-conjecture for completeness.