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139 papers · 1 filter
Moduli of atoms of complex projective varieties
Maxim Kontsevich, Szilard Szabo
The category of constituent pieces of Dubrovin connection of varieties is introduced and shown to be representable in affine space.
The monodromy of compact Lagrangian fibrations
Edward Varvak
We study the monodromy representations underlying compact Lagrangian fibrations. In the case where the associated period map is generically immersive, we prove that the mondromy re…
Multiplier ideals and klt singularities via (derived) splittings
Peter M. McDonald
Let be a normal, excellent, noetherian scheme over with a dualizing complex. In this note, we find an alternate characterization of the multipli…
Interpolation and moduli spaces of vector bundles on very general blowups of the projective plane
Izzet Coskun, Jack Huizenga
In this paper, we study certain moduli spaces of vector bundles on the blowup of the projective plane in at least 10 very general points. Moduli spaces of sheaves on general type s…
Teichmüller curves in hyperelliptic components of meromorphic strata
Martin Möller, Scott Mullane
We provide a complete classification of Teichmüller curves occurring in hyperelliptic components of the meromorphic strata of differentials. Using a non-existence criterion based o…
Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability
Junyan Zhao
In this paper, we study compactifications of the moduli of smooth del Pezzo surfaces using K-stability and the line arrangement. We construct K-moduli of log del Pezzo pairs with s…
Affine Subspace Concentration Conditions
Kuang-Yu Wu
We define a new notion of affine subspace concentration conditions for lattice polytopes, and prove that they hold for smooth and reflexive polytopes with barycenter at the origin.…
Finiteness for self-dual classes in integral variations of Hodge structure
Benjamin Bakker, Thomas W. Grimm, Christian Schnell +1
We generalize the finiteness theorem for the locus of Hodge classes with fixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge classes to self-dual classe…
When any three solutions are independent
James Freitag, Rémi Jaoui, Rahim Moosa
Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any number of distinct nonalgebraic solut…
Quantization of restricted Lagrangian subvarieties in positive characteristic
Joshua Mundinger
Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties X in positive characteristic which endow the Poisson bracket on X with the structure of a restricted Lie…
Saturation bounds for smooth varieties
Lawrence Ein, Huy Tai Ha, Robert Lazarsfeld
We prove bounds on the saturation degrees of homogeneous ideals (and their powers) defining smooth complex projective varieties. For example, we show that a classical statement due…
Arithmetic inflection formulae for linear series on hyperelliptic curves
Ethan Cotterill, Ignacio Darago, Changho Han
Over the complex numbers, Plücker's formula computes the number of inflection points of a linear series of projective dimension and degree on a curve of genus . Here we…
Singularities and syzygies of secant varieties of nonsingular projective curves
Lawrence Ein, Wenbo Niu, Jinhyung Park
In recent years, the equations defining secant varieties and their syzygies have attracted considerable attention. The purpose of the present paper is to conduct a thorough study o…
Covering gonalities of complete intersections in positive characteristic
Geoffrey Smith
We define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli-de Poi-Ein-Lazarsfeld-Ullery fo…
Stability of Normal Bundles of Space Curves
Izzet Coskun, Eric Larson, Isabel Vogt
In this paper, we prove that the normal bundle of a general Brill-Noether space curve of degree and genus is stable if and only if …
Moduli spaces of generalized hyperpolygons
Steven Rayan, Laura P. Schaposnik
We introduce the notion of generalized hyperpolygon, which arises as a representation, in the sense of Nakajima, of a comet-shaped quiver. We identify these representations with ri…
A refined Derived Torelli Theorem for Enriques surfaces
Chunyi Li, Howard Nuer, Paolo Stellari +1
We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from are isomorphic if their Kuznetsov components are equival…
Generalized B-Opers
Indranil Biswas, Laura P. Schaposnik, Mengxue Yang
Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients o…
MMP Via Wall-crossing for Moduli Spaces of Stable Sheaves on an Enriques surface
Howard Nuer, Kōta Yoshioka
We use wall-crossing in the Bridgeland stability manifold to systematically study the birational geometry of the moduli space of -semistable objects of class $…
The global moduli theory of symplectic varieties
Benjamin Bakker, Christian Lehn
We develop the global moduli theory of symplectic varieties in the sense of Beauville. We prove a number of analogs of classical results from the smooth case, including a global To…
o-minimal GAGA and a conjecture of Griffiths
Benjamin Bakker, Yohan Brunebarbe, Jacob Tsimerman
We prove a conjecture of Griffiths on the quasi-projectivity of images of period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop a…
Effective bounds on ampleness of cotangent bundles
Izzet Coskun, Eric Riedl
We prove that a general complete intersection of dimension , codimension and type in has ample cotangent bundle if and the $d_…
Birational superrigidity and K-stability of projectively normal Fano manifolds of index one
Fumiaki Suzuki
We prove that every projectively normal Fano manifold in of index , codimension and dimension is birationally superrigid and K-stable. This re…
-signature under birational morphisms
Linquan Ma, Thomas Polstra, Karl Schwede +1
We study -signature under proper birational morphisms , showing that -signature strictly increases for small morphisms or if . In certain cases,…