Results 1  10
of
220
Polyhedral algebras, arrangements of toric varieties, and their groups
"... We investigate the automorphism groups of graded algebras defined by lattice polyhedral complexes and of the corresponding projective varieties, which form arrangements of projective toric varieties. These groups are polyhedral versions of the general and projective linear groups. It is shown that f ..."
Abstract

Cited by 15 (9 self)
 Add to MetaCart
We investigate the automorphism groups of graded algebras defined by lattice polyhedral complexes and of the corresponding projective varieties, which form arrangements of projective toric varieties. These groups are polyhedral versions of the general and projective linear groups. It is shown
Polyhedral Divisors and Algebraic Torus Actions
 Math. Ann
, 2006
"... Abstract. We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our approach extends classical cone constructions of Dolgachev, Demazure and Pinkham to the multigraded case, ..."
Abstract

Cited by 50 (9 self)
 Add to MetaCart
Abstract. We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our approach extends classical cone constructions of Dolgachev, Demazure and Pinkham to the multigraded case
Higher polyhedral Kgroups
"... Abstract. We define higher polyhedral Kgroups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin’s theory and Quillen’s + construction are developed. In the special case of algebras associated with unit simplices one recovers the ..."
Abstract

Cited by 5 (5 self)
 Add to MetaCart
Abstract. We define higher polyhedral Kgroups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin’s theory and Quillen’s + construction are developed. In the special case of algebras associated with unit simplices one recovers
On the 'Piano Movers' Problem II. General Techniques for Computing Topological Properties of Real Algebraic Manifolds
, 1982
"... This paper continues the discussion, begun in [SS], of the following problem, which arises in robotics: Given a collection of bodies B, which may be hinged, i.e. may allow internal motion around various joints, and given a region bounded by a collection of polyhedral or other simple walls, decide ..."
Abstract

Cited by 228 (9 self)
 Add to MetaCart
This paper continues the discussion, begun in [SS], of the following problem, which arises in robotics: Given a collection of bodies B, which may be hinged, i.e. may allow internal motion around various joints, and given a region bounded by a collection of polyhedral or other simple walls, decide
Polyhedral Methods in Numerical Algebraic Geometry
, 2008
"... In numerical algebraic geometry witness sets are numerical representations of positive dimensional solution sets of polynomial systems. Considering the asymptotics of witness sets we propose certificates for algebraic curves. These certificates are the leading terms of a Puiseux series expansion of ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
In numerical algebraic geometry witness sets are numerical representations of positive dimensional solution sets of polynomial systems. Considering the asymptotics of witness sets we propose certificates for algebraic curves. These certificates are the leading terms of a Puiseux series expansion
Merging BSP Trees Yields Polyhedral Set Operations
 COMPUTER GRAPHICS
, 1990
"... BSP trees have been shown to provide an effective repretentation of polyhedra through the use of spatial subdivision,;nd are an alternative to the topologically based breps. While?sp tree algorithms are knownfor a number of important opera:ions, such as rendering, no previous work on bsp trees has ..."
Abstract

Cited by 100 (2 self)
 Add to MetaCart
has trovided the capability of performing boolean set operations tetween two objects represented by bsp trees, i.e. there has leen no closed boolean algebra when using bsp lrees. This pa.er presents the algorithms required to perform such opera:ions. In doing so, a distinction is made between
Hopf algebra deformations of binary polyhedral groups
"... Abstract. We show that semisimple Hopf algebras having a selfdual faithful irreducible comodule of dimension 2 are always obtained as abelian extensions with quotient Z2. We prove that nontrivial Hopf algebras arising in this way can be regarded as deformations of binary polyhedral groups and descr ..."
Abstract

Cited by 15 (8 self)
 Add to MetaCart
Abstract. We show that semisimple Hopf algebras having a selfdual faithful irreducible comodule of dimension 2 are always obtained as abelian extensions with quotient Z2. We prove that nontrivial Hopf algebras arising in this way can be regarded as deformations of binary polyhedral groups
A REMARK ON ALGEBRAIC SURFACES WITH POLYHEDRAL MORI CONE
, 1998
"... Abstract. We denote by FPMC the class of all nonsingular projective algebraic surfaces X over C with a finite polyhedral Mori cone NE(X) ⊂ NS(X) ⊗ R. If ρ(X) = rk NS(X) ≥ 3, then the set Exc(X) of all exceptional curves on X ∈ FPMC is finite and generates NE(X). Let δE(X) be the maximum of (−E2 ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
Abstract. We denote by FPMC the class of all nonsingular projective algebraic surfaces X over C with a finite polyhedral Mori cone NE(X) ⊂ NS(X) ⊗ R. If ρ(X) = rk NS(X) ≥ 3, then the set Exc(X) of all exceptional curves on X ∈ FPMC is finite and generates NE(X). Let δE(X) be the maximum of (−E
Results 1  10
of
220