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010   $a1-4008-8252-4
024 7 $a10.1515/9781400882526
035   $a(CKB)3710000000622814
035   $a(MiAaPQ)EBC4738795
035   $a(DE-B1597)468045
035   $a(OCoLC)979747116
035   $a(DE-B1597)9781400882526
035   $a(PPN)256613079
035   $a(EXLCZ)993710000000622814
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aIntroduction to Toric Varieties. (AM-131), Volume 131 /$fWilliam Fulton
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1993
215   $a1 online resource (171 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v314
311   $a0-691-03332-3 
311   $a0-691-00049-2 
320   $aIncludes bibliographical references and indexes.
327   $tFrontmatter -- $tContents -- $tPreface -- $tErrata -- $tChapter 1. Definitions and examples -- $tChapter 2. Singularities and compactness -- $tChapter 3. Orbits, topology, and line bundles -- $tChapter 4. Moment maps and the tangent bundle -- $tChapter 5. Intersection theory -- $tNotes -- $tReferences -- $tIndex of Notation -- $tIndex
330   $aToric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are "ed without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.
410  0$aAnnals of mathematics studies ;$vno. 131.
410  0$aWilliam H. Roever lectures in geometry.
606   $aToric varieties
610   $aAddition.
610   $aAffine plane.
610   $aAffine space.
610   $aAffine variety.
610   $aAlexander Grothendieck.
610   $aAlexander duality.
610   $aAlgebraic curve.
610   $aAlgebraic group.
610   $aAtiyah?Singer index theorem.
610   $aAutomorphism.
610   $aBetti number.
610   $aBig O notation.
610   $aCharacteristic class.
610   $aChern class.
610   $aChow group.
610   $aCodimension.
610   $aCohomology.
610   $aCombinatorics.
610   $aCommutative property.
610   $aComplete intersection.
610   $aConvex polytope.
610   $aConvex set.
610   $aCoprime integers.
610   $aCotangent space.
610   $aDedekind sum.
610   $aDimension (vector space).
610   $aDimension.
610   $aDirect proof.
610   $aDiscrete valuation ring.
610   $aDiscrete valuation.
610   $aDisjoint union.
610   $aDivisor (algebraic geometry).
610   $aDivisor.
610   $aDual basis.
610   $aDual space.
610   $aEquation.
610   $aEquivalence class.
610   $aEquivariant K-theory.
610   $aEuler characteristic.
610   $aExact sequence.
610   $aExplicit formula.
610   $aFacet (geometry).
610   $aFundamental group.
610   $aGraded ring.
610   $aGrassmannian.
610   $aH-vector.
610   $aHirzebruch surface.
610   $aHodge theory.
610   $aHomogeneous coordinates.
610   $aHomomorphism.
610   $aHypersurface.
610   $aIntersection theory.
610   $aInvertible matrix.
610   $aInvertible sheaf.
610   $aIsoperimetric inequality.
610   $aLattice (group).
610   $aLeray spectral sequence.
610   $aLimit point.
610   $aLine bundle.
610   $aLine segment.
610   $aLinear subspace.
610   $aLocal ring.
610   $aMathematical induction.
610   $aMixed volume.
610   $aModuli space.
610   $aMoment map.
610   $aMonotonic function.
610   $aNatural number.
610   $aNewton polygon.
610   $aOpen set.
610   $aPicard group.
610   $aPick's theorem.
610   $aPolytope.
610   $aProjective space.
610   $aQuadric.
610   $aQuotient space (topology).
610   $aRegular sequence.
610   $aRelative interior.
610   $aResolution of singularities.
610   $aRestriction (mathematics).
610   $aResultant.
610   $aRiemann?Roch theorem.
610   $aSerre duality.
610   $aSign (mathematics).
610   $aSimplex.
610   $aSimplicial complex.
610   $aSimultaneous equations.
610   $aSpectral sequence.
610   $aSubgroup.
610   $aSubset.
610   $aSummation.
610   $aSurjective function.
610   $aTangent bundle.
610   $aTheorem.
610   $aTopology.
610   $aToric variety.
610   $aUnit disk.
610   $aVector space.
610   $aWeil conjecture.
610   $aZariski topology.
615  0$aToric varieties.
676   $a516.3/53
700   $aFulton$b William, $041611
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154749903321
996   $aIntroduction to Toric Varieties. (AM-131), Volume 131$92787594
997   $aUNINA