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Correspondences between convex geometry and complex geometry [PDF]
Épijournal de Géométrie Algébrique, 2017 We present several analogies between convex geometry and the theory of holomorphic line bundles on smooth projective varieties or K\"ahler manifolds. We study the relation between positive products and mixed volumes.
Brian Lehmann, Jian Xiao
doaj +1 more source
Local cohomology of logarithmic forms [PDF]
, 2012 Let Y be a divisor on a smooth algebraic variety X. We investigate the geometry of the Jacobian scheme of Y, homological invariants derived from logarithmic differential forms along Y, and their relationship with the property that Y is a free divisor ...
Denham, Graham +4 more
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A Dual of the Chow Transformation
Complex Manifolds, 2018 We define a dual of the Chow transformation of currents on the complex projective space. This transformation factorizes a left inverse of the Chow transformation and its composition with the Chow transformation is a right inverse of a linear diferential ...
Méo Michel
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Projectivity and Birational Geometry of Bridgeland moduli spaces [PDF]
, 2012 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 condition.
Bayer, Arend, Macri, Emanuele
core +5 more sources
Singularities and Semistable Degenerations for Symplectic Topology [PDF]
, 2017 We overview our recent work defining and studying normal crossings varieties and subvarieties in symplectic topology. This work answers a question of Gromov on the feasibility of introducing singular (sub)varieties into symplectic topology in the case of
McLean, Mark +2 more
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Rational curves on fibered Calabi-Yau manifolds [PDF]
, 2018 We show that a smooth projective complex manifold of dimension greater than two endowed with an elliptic fiber space structure and with finite fundamental group always contains a rational curve, provided its canonical bundle is relatively trivial.
Diverio, Simone +2 more
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Algebraic bounds on analytic multiplier ideals [PDF]
, 2013 Given a pseudo-effective divisor L we construct the diminished ideal of L, a "continuous" extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary.
Lehmann, Brian
core +2 more sources
Sheaves on Toric Varieties for Physics [PDF]
, 1997 In this paper we give an inherently toric description of a special class of sheaves (known as equivariant sheaves) over toric varieties, due in part to A. A. Klyachko.
Knutson, A., Sharpe, E.
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Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound
, 2017 It was shown by Massey that linear complementary dual (LCD for short) codes are asymptotically good. In 2004, Sendrier proved that LCD codes meet the asymptotic Gilbert-Varshamov (GV for short) bound.
Jin, Lingfei, Xing, Chaoping
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Birationally superrigid cyclic triple spaces
, 2004 We prove the birational superrigidity and the nonrationality of a cyclic triple cover of $\mathbb{P}^{2n}$ branched over a nodal hypersurface of degree $3n$ for $n\ge 2$.
Cheltsov, Ivan
core +2 more sources