Results 21 to 30 of about 64 (64)

Complements and coregularity of Fano varieties

Forum of Mathematics, Sigma
We study the relation between the coregularity, the index of log Calabi–Yau pairs and the complements of Fano varieties. We show that the index of a log Calabi–Yau pair $(X,B)$ of coregularity $1$ is at most $120\lambda ^2$ , where
Fernando Figueroa, Stefano Filipazzi, Joaquín Moraga, Junyao Peng   +3 more
doaj   +1 more source

IGUSA’S CONJECTURE FOR EXPONENTIAL SUMS: OPTIMAL ESTIMATES FOR NONRATIONAL SINGULARITIES

Forum of Mathematics, Pi, 2019
We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa’s conjecture on exponential sums, with the log canonical threshold in the exponent of ...
RAF CLUCKERS, MIRCEA MUSTAŢĂ, KIEN HUU NGUYEN   +2 more
doaj   +1 more source

Boundedness of slc degenerations of polarized log Calabi–Yau pairs

Forum of Mathematics, Sigma
Given a family of pairs over a smooth curve whose general fiber is a log Calabi–Yau pair in a fixed bounded family, suppose there exists a divisor on the family whose restriction on a general fiber is ample with bounded volume.
Junpeng Jiao
doaj   +1 more source

On the MMP for rank one foliations on threefolds

Forum of Mathematics, Pi
We prove existence of flips for log canonical foliated pairs of rank one on a ${\mathbb Q}$ -factorial projective klt threefold. This, in particular, provides a proof of the existence of a minimal model for a rank one foliation on a threefold for a
Paolo Cascini, Calum Spicer
doaj   +1 more source

Equivariant geometry of singular cubic threefolds

Forum of Mathematics, Sigma
We study linearizability of actions of finite groups on singular cubic threefolds, using cohomological tools, intermediate Jacobians, Burnside invariants, and the equivariant Minimal Model Program.
Ivan Cheltsov, Yuri Tschinkel, Zhijia Zhang   +2 more
doaj   +1 more source

Optimal bounds in Bend-and-Break

Forum of Mathematics, Pi
We improve the Bend-and-Break result of Miyaoka and Mori by establishing the optimal degree bound. Our result also yields optimal bounds on lengths of extremal rays of log canonical pairs.
Eric Jovinelly, Brian Lehmann, Eric Riedl   +2 more
doaj   +1 more source

Pathological MMP singularities as αp-quotients

Forum of Mathematics, Sigma
We construct pathological examples of MMP singularities in every positive characteristic using quotients by $\alpha _p$ -actions. In particular, we obtain non- $S_3$ terminal singularities, as well as locally stable (respectively stable ...
Quentin Posva
doaj   +1 more source

On $G$-birational rigidity of del Pezzo surfaces [PDF]

Épijournal de Géométrie Algébrique
Let $G$ be a finite group and $H\subseteq G$ be its subgroup. We prove that if a smooth del Pezzo surface over an algebraically closed field is $H$-birationally rigid then it is also $G$-birationally rigid, answering a geometric version of Koll\'{a}r's ...
Egor Yasinsky
doaj   +1 more source

Optimal bound for singularities on Fano type fibrations of relative dimension one

Forum of Mathematics, Sigma
Let $\pi :X\rightarrow Z$ be a Fano type fibration with $\dim X-\dim Z=d$ and let $(X,B)$ be an $\epsilon $ -lc pair with $K_X+B\sim _{\mathbb {R}} 0/Z$ . The canonical bundle formula gives $(Z,B_Z+M_Z)$ where $
Bingyi Chen
doaj   +1 more source

Bounding geometrically integral del Pezzo surfaces

Forum of Mathematics, Sigma
We prove several boundedness statements for geometrically integral normal del Pezzo surfaces X over arbitrary fields. We give an explicit sharp bound on the irregularity if X is canonical or regular.
Fabio Bernasconi, Gebhard Martin
doaj   +1 more source