153 citations · 589 across the 21 of their papers we have counts for
25 papers
Mukai models of Fano varieties
Arend Bayer, Alexander Kuznetsov, Emanuele Macrì
We give a self-contained and simplified proof of Mukai's classification of prime Fano threefolds of index 1 and genus with at most Gorenstein factorial terminal singulari…
Mukai bundles on Fano threefolds
Arend Bayer, Alexander Kuznetsov, Emanuele Macrì
We give a proof of Mukai's Theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literat…
Brill-Noether theory of Hilbert schemes of points on surfaces
Arend Bayer, Huachen Chen, Qingyuan Jiang
We show that Brill--Noether loci in Hilbert scheme of points on a smooth connected surface are non-empty whenever their expected dimension is positive, and that they are irredu…
Kuznetsov's Fano threefold conjecture via K3 categories and enhanced group actions
Arend Bayer, Alexander Perry
We settle the last open case of Kuznetsov's conjecture on the derived categories of Fano threefolds. Contrary to the original conjecture, we prove the Kuznetsov components of quart…
The unreasonable effectiveness of wall-crossing in algebraic geometry
Arend Bayer, Emanuele Macrì
We survey applications of Bridgeland stability conditions in algebraic geometry and discuss open questions for future research.
The desingularization of the theta divisor of a cubic threefold as a moduli space
Arend Bayer, Sjoerd Beentjes, Soheyla Feyzbakhsh +4
We show that the moduli space of Gieseker stable sheaves on a smooth cubic threefold with Chern character is smooth and of dimensi…
Stability conditions in families
Arend Bayer, Martí Lahoz, Emanuele Macrì +3
We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by…
Brill-Noether theory for curves on generic abelian surfaces
Arend Bayer, Chunyi Li
We completely describe the Brill-Noether theory for curves in the primitive linear system on generic abelian surfaces, in the following sense: given integers and , consider…
Stability conditions on Kuznetsov components
Arend Bayer, Martí Lahoz, Emanuele Macrì +1
We introduce a general method to induce Bridgeland stability conditions on semiorthogonal components of triangulated categories. In particular, we prove the existence of Bridgeland…
A short proof of the deformation property of Bridgeland stability conditions
Arend Bayer
The key result in the theory of Bridgeland stability conditions is the property that they form a complex manifold. This comes from the fact that given any small deformation of the…
Wall-Crossing implies Brill-Noether. Applications of stability conditions on surfaces
Arend Bayer
Over the last few years, wall-crossing for Bridgeland stability conditions has led to a large number of results in algebraic geometry, particular on birational geometry of moduli s…
Nef divisors for moduli spaces of complexes with compact support
Arend Bayer, Alastair Craw, Ziyu Zhang
In [BM14b], the first author and Macrì constructed a family of nef divisors on any moduli space of Bridgeland-stable objects on a smooth projective variety X. In this article, we e…
The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
Arend Bayer, Emanuele Macrì, Paolo Stellari
We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient…
Derived automorphism groups of K3 surfaces of Picard rank 1
Arend Bayer, Tom Bridgeland
We give a complete description of the group of exact autoequivalences of the bounded derived category of coherent sheaves on a K3 surface of Picard rank 1. We do this by proving th…
Mori cones of holomorphic symplectic varieties of K3 type
Arend Bayer, Brendan Hassett, Yuri Tschinkel
We determine the Mori cone of holomorphic symplectic varieties deformation equivalent to the punctual Hilbert scheme on a K3 surface. Our description is given in terms of Markman's…
MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations
Arend Bayer, Emanuele Macrì
We use wall-crossing with respect to Bridgeland stability conditions to systematically study the birational geometry of a moduli space M of stable sheaves on a K3 surface X: 1. We…
Projectivity and Birational Geometry of Bridgeland moduli spaces
Arend Bayer, Emanuele Macri
We construct a family of nef divisor classes on every moduli space of stable complexes in the sense of Bridgeland. This divisor class varies naturally with the Bridgeland stability…
Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture
Arend Bayer, Aaron Bertram, Emanuele Macri +1
We apply a conjectured inequality on third chern classes of stable two-term complexes on threefolds to Fujita's conjecture. More precisely, the inequality is shown to imply a Reide…
Bridgeland Stability conditions on threefolds I: Bogomolov-Gieseker type inequalities
Arend Bayer, Emanuele Macri, Yukinobu Toda
We construct new t-structures on the derived category of coherent sheaves on smooth projective threefolds. We conjecture that they give Bridgeland stability conditions near the lar…
The space of stability conditions on the local projective plane
Arend Bayer, Emanuele Macri
We study the space of stability conditions on the total space of the canonical bundle over the projective plane. We explicitly describe a chamber of geometric stability conditions,…
Polynomial Bridgeland stability conditions and the large volume limit
Arend Bayer
We introduce the notion of a polynomial stability condition, generalizing Bridgeland stability conditions on triangulated categories. We construct and study a family of polynomial…
Quantum cohomology of [C^N/μ_r]
Arend Bayer, Charles Cadman
We give a construction of the moduli space of stable maps to the classifying stack Bμ_r of a cyclic group by a sequence of r-th root constructions on M_{0, n}. We prove a closed fo…
Stability Conditions, Wall-crossing and weighted Gromov-Witten Invariants
Arend Bayer, Yuri I. Manin
We extend B. Hassett's theory of weighted stable pointed curves ([Has03]) to weighted stable maps. The space of stability conditions is described explicitly, and the wall-crossing…
Semisimple Quantum Cohomology and Blow-ups
Arend Bayer
Using results of Gathmann, we prove the following theorem: If a smooth projective variety X has generically semisimple (p,p)-quantum cohomology, then the same is true for the blow-…