Articles

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The Structure of Bivariate Rational Hypergeometric Functions (with Alicia Dickenstein and Fernando Villegas), International Mathematics Research Notices (2010)

We describe the structure of all codimension-2 lattice configurations A which admit a stable rational...

 

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Infinitesimal variations of Hodge structure at infinity (with J Fernandez), Geometriae Dedicata (2009)

By analyzing the local and infinitesimal behavior of degenerating polarized variations of Hodge structure the...

 

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Mixed Lefschetz Theorems and Hodge-Riemann Bilinear Relations, International Mathematic Research Notices (2008)

The Hard Lefschetz Theorem (HLT) and the Hodge–Riemann bilinear relations (HRR) hold in various contexts:...

 

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Complete intersections in toric ideals (with R Curran and A Dickenstein), Proceedings of the American Mathematical Society (2007)

We present examples that show that in dimension higher than one or...

 

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Counting solutions to binomial complete intersections (with A Dickenstein), Journal of Complexity (2007)

We study the problem of counting the total number of affine solutions of a system...

 

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Restriction of A-discriminants and dual defect toric varieties (with R Curran), Journal of Symbolic Computation (2007)

We study the A-discriminant of toric varieties....

 

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Complete Intersections in Toric Ideals (with Raymond Curran and Alicia Dickenstein), Proceedings of the American Mathematical Society (2005)

We present examples which show that in dimension higher than one or codimension higher than...

 

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Planar configurations of lattice vectors and GKZ-rational toric fourfolds in P-6 (with A Dickenstein), Journal of Algebraic Combinatorics (2004)

We introduce a notion of balanced configurations of vectors. This is motivated by the study...

 

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Frobenius modules and Hodge asymptotics (with J Fernandez), Communications inMathematical Physics (2003)

We exhibit a direct correspondence between the potential defining the H1,1 small quantum module structure...

 

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Binomial residues (with A Dickenstein and B Sturmfels), Annales De L Institut Fourier (2002)

A binomial residue is a rational function defined by a hypergeometric integral whose kernel is...

 

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Rational hypergeometric functions (with A Dickenstein and B Sturmfels), Composito Mathematica (2001)

Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities...

 

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The A-hypergeometric system associated with a monomial curve (with C D'Andrea and A Dickenstein), Duke Mathematical Journal (1999)
 

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The A-hypergeometric System Associated with a Monomial Curve (with Carlos D’Andrea and Alicia Dickenstein), Duke Mathematical Journal (1998)
 

A global view of residues in the torus (with A Dickenstein), Journal of Pure and Applied Algebra (1997)

We study the total sum of Grothendieck residues of a Laurent polynomial relative to a...

 

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Residues and Resultants (with Alicia Dickenstein and Bernd Sturmfels), Journal of Mathematical Sciences (1997)

Resultants, Jacobians and residues are basic invariants of multivariate polynomial systems. We examine their interrelations...

 

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Residues in toric varieties (with D Cox and A Dickenstein), Composito Mathematica (1997)

We study residues on a complete toric variety X, which are defined in terms of...

 

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On the locus of hodge classes (with P. Deligne and A. Kaplan), Journal of the American Mathematical Society (1995)

Let S be a nonsingular complex algebraic variety and V a polarized variation of Hodge...

 

Degenerating variations of hodge structure (with A KAPLAN), Asterisque (1989)
 

L2 and intersection cohomologies for a polarizable variation of hodge structure (with A KAPLAN and W SCHMID), Inventiones Mathematicae (1987)
 

Some remarks on L2 and intersection cohomologies (with A Kaplan and W Schmid), Lecture Notes in Mathematics (1987)
 

Varization of polarized hodge structure - Asymptotics and monodromy (with A Kaplan and W Schmid), Lecture Notes in Mathematics (1987)
 

Degeneration of hodge-structures (with A KAPLAN and W SCHMID), Annals of Mathematics (1986)

An abstract for this item is not available.

 

On the L2-cohomology and the intersection cohomology of variations of hodge-structures (with A Kaplan), Comptes Rendus De L Academie Des Sciences Serie I-Mathematique (1985)
 

Mixed Hodge-structures, compactification and monodromy weight filtration, Annals of Mathematics Studies (1984)
 

Polarized mixed hodge-structures and the local monodromy of a variation of hodge structure (with A Kaplan), Inventiones Mathematicae (1982)

Some of the work on this paper was done while the first author was on...

 

On the Local Monodromy of a Variation of Hodge Structure (with A KAPLAN), Bulletin of the American Mathematical Society (1981)
 

Other

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Asymptotic Hodge theory and quantum products (with Javier Fernandez), Mathematics and Statistics Department Faculty Publication Series (2000)

Assuming suitable convergence properties for the Gromov-Witten potential of a Calabi-Yau manifold $X$ one may...

 

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Computing Multidimensional Residues (with Alicia Dickenstein and Bernd Sturmfels), Mathematics and Statistics Department Faculty Publication Series (1994)

Given n polynomials in n variables with a finite number of complex roots, for any...