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Enumerative Geometry
"... Notes for a class taught at the University of Kaiserslautern 2003/2004 — preliminary version — CONTENTS ..."
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Notes for a class taught at the University of Kaiserslautern 2003/2004 — preliminary version — CONTENTS
An Enumerative Geometry for . . .
, 2008
"... A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without the diagonals). A ma ..."
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A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without the diagonals). A magilatin labelling is like a magic labelling but the values need be distinct only within each set. We show that the number of n×n magic or magilatin labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in the square. Our results differ from previous ones because we require that the entries in the square all be different from each other, and because we derive our results not by ad hoc reasoning but from a general theory of counting lattice points in rational insideout polytopes. We also generalize from set systems to rational linear forms.
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
Towards an enumerative geometry of the moduli space of curves
 in Arithmetic and Geometry
, 1983
"... The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring for the moduli space M g of curves of genus g and its compactification.M 9, defining what seem to be ..."
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The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring for the moduli space M g of curves of genus g and its compactification.M 9, defining what seem to be
Enumerative geometry and knot invariants
, 2003
"... We review the string/gauge theory duality relating ChernSimons theory and topological strings on noncompact CalabiYau manifolds, as well as its mathematical implications for knot invariants and enumerative geometry. ..."
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We review the string/gauge theory duality relating ChernSimons theory and topological strings on noncompact CalabiYau manifolds, as well as its mathematical implications for knot invariants and enumerative geometry.
Enumerative Geometry For Real Varieties
 Proc. of Symp. Pur. Math
"... Introduction Of the geometric figures in a given family satisfying real conditions, some figures are real while the rest occur in complex conjugate pairs, and the distribution of the two types depends subtly upon the configuration of the conditions. Despite this difficulty, applications ([7],[28],[ ..."
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],[28],[32]) may demand real solutions. Fulton [11] asked how many solutions of an enumerative problem can be real, and we consider a special case of his question: Given a problem of enumerative geometry, are there real conditions such that every figure satisfying them is real? Such an enumerative problem is fully
Enumerative geometry of hyperelliptic plane curves
 J. Algebraic Geom
"... In recent years there has been a tremendous amount of progress on classical problems in enumerative geometry. This has largely been a result of new ideas and motivation for these problems coming from theoretical physics. In particular, the theory of GromovWitten invariants ..."
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In recent years there has been a tremendous amount of progress on classical problems in enumerative geometry. This has largely been a result of new ideas and motivation for these problems coming from theoretical physics. In particular, the theory of GromovWitten invariants
On the Enumerative Geometry of Aspect Graphs
"... Most of the work achieved thus far on aspect graphs has concentrated on the design of algorithms for computing the representation. After reviewing how the space of viewpoints can be partitioned in viewequivalent cells, we work in this paper on a more theoretical level to give enumerative properties ..."
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Most of the work achieved thus far on aspect graphs has concentrated on the design of algorithms for computing the representation. After reviewing how the space of viewpoints can be partitioned in viewequivalent cells, we work in this paper on a more theoretical level to give enumerative
The Enumerative Geometry of Hyperplane Arrangements
"... We study enumerative questions on the moduli space M(L) of hyperplane arrangements with a given intersection lattice L. Mnëv’s universality theorem suggests that these moduli spaces can be arbitrarily complicated; indeed it is even difficult to compute the dimensionD = dimM(L). EmbeddingM(L) in a ..."
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We study enumerative questions on the moduli space M(L) of hyperplane arrangements with a given intersection lattice L. Mnëv’s universality theorem suggests that these moduli spaces can be arbitrarily complicated; indeed it is even difficult to compute the dimensionD = dimM(L). EmbeddingM(L) in a
Notes on Enumerative Geometry
"... 1 Lines in affine/projective spaces............................. 5 ..."
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