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Search: All articles in the CJM digital archive with keyword toric

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1. CJM Online first

Nohara, Yuichi; Ueda, Kazushi
 Goldman systems and bending systems We show that the moduli space of parabolic bundles on the projective line and the polygon space are isomorphic, both as complex manifolds and symplectic manifolds equipped with structures of completely integrable systems, if the stability parameters are small. Keywords:toric degenerationCategories:53D30, 14H60

2. CJM 2012 (vol 65 pp. 634)

Mezzetti, Emilia; Miró-Roig, Rosa M.; Ottaviani, Giorgio
 Laplace Equations and the Weak Lefschetz Property We prove that $r$ independent homogeneous polynomials of the same degree $d$ become dependent when restricted to any hyperplane if and only if their inverse system parameterizes a variety whose $(d-1)$-osculating spaces have dimension smaller than expected. This gives an equivalence between an algebraic notion (called Weak Lefschetz Property) and a differential geometric notion, concerning varieties which satisfy certain Laplace equations. In the toric case, some relevant examples are classified and as byproduct we provide counterexamples to Ilardi's conjecture. Keywords:osculating space, weak Lefschetz property, Laplace equations, toric threefoldCategories:13E10, 14M25, 14N05, 14N15, 53A20

3. CJM 2010 (vol 62 pp. 1293)

Kasprzyk, Alexander M.
 Canonical Toric Fano Threefolds An inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are $674,\!688$ such varieties. Keywords:toric, Fano, threefold, canonical singularities, convex polytopesCategories:14J30, 14J30, 14M25, 52B20

4. CJM 2007 (vol 59 pp. 981)

Jiang, Yunfeng
 The Chen--Ruan Cohomology of Weighted Projective Spaces In this paper we study the Chen--Ruan cohomology ring of weighted projective spaces. Given a weighted projective space ${\bf P}^{n}_{q_{0}, \dots, q_{n}}$, we determine all of its twisted sectors and the corresponding degree shifting numbers. The main result of this paper is that the obstruction bundle over any 3\nobreakdash-multi\-sector is a direct sum of line bundles which we use to compute the orbifold cup product. Finally we compute the Chen--Ruan cohomology ring of weighted projective space ${\bf P}^{5}_{1,2,2,3,3,3}$. Keywords:Chen--Ruan cohomology, twisted sectors, toric varieties, weighted projective space, localizationCategories:14N35, 53D45

5. CJM 2004 (vol 56 pp. 1094)

Thomas, Hugh
 Cycle-Level Intersection Theory for Toric Varieties This paper addresses the problem of constructing a cycle-level intersection theory for toric varieties. We show that by making one global choice, we can determine a cycle representative for the intersection of an equivariant Cartier divisor with an invariant cycle on a toric variety. For a toric variety defined by a fan in $N$, the choice consists of giving an inner product or a complete flag for $M_\Q= \Qt \Hom(N,\mathbb{Z})$, or more generally giving for each cone $\s$ in the fan a linear subspace of $M_\Q$ complementary to $\s^\perp$, satisfying certain compatibility conditions. We show that these intersection cycles have properties analogous to the usual intersections modulo rational equivalence. If $X$ is simplicial (for instance, if $X$ is non-singular), we obtain a commutative ring structure to the invariant cycles of $X$ with rational coefficients. This ring structure determines cycles representing certain characteristic classes of the toric variety. We also discuss how to define intersection cycles that require no choices, at the expense of increasing the size of the coefficient field. Keywords:toric varieties, intersection theoryCategories:14M25, 14C17

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