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405
Kodaira dimension and zeros of holomorphic oneforms
 Ann. of Math
, 2014
"... Abstract We show that every holomorphic oneform on a smooth complex projective variety of general type must vanish at some point. The proof uses generic vanishing theory for Hodge modules on abelian varieties. ..."
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Cited by 3 (3 self)
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Abstract We show that every holomorphic oneform on a smooth complex projective variety of general type must vanish at some point. The proof uses generic vanishing theory for Hodge modules on abelian varieties.
HOLOMORPHIC ONEFORMS ON VARIETIES OF GENERAL TYPE
, 2004
"... It has been conjectured that varieties of general type do not admit nowhere vanishing holomorphic oneforms. We confirm this conjecture for smooth minimal varieties and for varieties whose Albanese variety is simple. ..."
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Cited by 1 (0 self)
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It has been conjectured that varieties of general type do not admit nowhere vanishing holomorphic oneforms. We confirm this conjecture for smooth minimal varieties and for varieties whose Albanese variety is simple.
On holomorphic oneforms transverse to closed hypersurfaces
, 2003
"... presented by Marcio Soares In this note we announce some achievements in the study of holomorphic distributions admitting transverse closed real hypersurfaces. We consider a domain with smooth boundary in the complex affine space of dimension two or greater. Assume that the domain satisfies some coh ..."
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is equal to the sum of indexes of the oneform at its singular points inside the domain. This result has several consequences and applies, for instance, to the study of codimension one holomorphic foliations transverse to spheres.
OneForms
"... Abstract. Here we introduce multivariate tensorbased surface morphometry using holomorphic oneforms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic onefo ..."
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Abstract. Here we introduce multivariate tensorbased surface morphometry using holomorphic oneforms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic oneforms
CRM Monograph Series Volume 20
"... surface X is a compact oriented twodimensional manifold. These are just surfaces of genus g and elementary topology tells us that the homology group, H1 (X,Z), is a free abelian group with 2g generators A1,B1,... Ag,Bg, which can be chosen so that the self intersections Ai ×Aj=Bi×Bj=0 and Ai ×Bj=δi ..."
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=δij. If one imposes the structure of a Riemann surface on X, i.e. a complex structure, for each homology basis Ai,Bi as above there is a unique basis ω1,...ωg of the complex vector space of holomorphic oneforms with the property that for all 1 ≤ i,k ≤ g ω k = δ ik. A i Having normalized the integrals
ON THE GALOIS REDUCIBILITY OF A GERM OF QUASIHOMOGENEOUS FOLIATION
"... From recent developments in non linear dierential Galois theory, we have now three equivalent denitions for the Galois reducibility of a codimension one foliation dened by a germ of holomorphic oneform!: the rst one is related to GodbillonVey sequences: there exists a nite sequence of ..."
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From recent developments in non linear dierential Galois theory, we have now three equivalent denitions for the Galois reducibility of a codimension one foliation dened by a germ of holomorphic oneform!: the rst one is related to GodbillonVey sequences: there exists a nite sequence of
Symplectic structures and volume elements in the function space for the cubic Schrödinger equation
"... Abstract. We consider various trace formulas for the cubic Schrödinger equation in the space of infinitely smooth functions subject to periodic boundary conditions. The formulas relate conventional integrals of motion to the periods of some Abelian differentials (holomorphic oneforms) on the spectr ..."
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Cited by 7 (2 self)
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Abstract. We consider various trace formulas for the cubic Schrödinger equation in the space of infinitely smooth functions subject to periodic boundary conditions. The formulas relate conventional integrals of motion to the periods of some Abelian differentials (holomorphic oneforms
Genus zero surface conformal mapping and its application to brain surface mapping
 IEEE Transactions on Medical Imaging
, 2004
"... Abstract—We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic oneforms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping betwe ..."
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Cited by 188 (78 self)
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Abstract—We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic oneforms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping
Fivebranes, Membranes And NonPerturbative String Theory
, 1995
"... Nonperturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a CalabiYau space are derived and found to contain order e \Gamma1=g s contributions, where g s is the string coupling. The computation reduces to a weighted sum of supersymmetric extrema ..."
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Cited by 387 (6 self)
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extremal maps of strings, membranes and fivebranes into the CalabiYau space, all three of which enter on equal footing. It is shown that a supersymmetric 3cycle is one for which the pullback of the Kahler form vanishes and the pullback of the holomorphic threeform is a constant multiple of the volume
Computing conformal structures of surfaces
 Communications in Information and Systems
, 2002
"... Abstract. This paper solves the problem of computing conformal structures of general 2manifolds represented as triangular meshes. We approximate the De Rham cohomology by simplicial cohomology and represent the LaplaceBeltrami operator, the Hodge star operator by linear systems. A basis of holomorp ..."
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Cited by 67 (17 self)
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of holomorphic oneforms is constructed explicitly. We then obtain a period matrix by integrating holomorphic differentials along a homology basis. We also study the global conformal mappings between genus zero surfaces and spheres, and between general surfaces and planes. Our method of computing conformal
Results 1  10
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405