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Advances in Algebraic Geometry Motivated by Physics
 
Edited by: Emma Previato Boston University, Boston, MA
Advances in Algebraic Geometry Motivated by Physics
eBook ISBN:  978-0-8218-7866-8
Product Code:  CONM/276.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Advances in Algebraic Geometry Motivated by Physics
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Advances in Algebraic Geometry Motivated by Physics
Edited by: Emma Previato Boston University, Boston, MA
eBook ISBN:  978-0-8218-7866-8
Product Code:  CONM/276.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 2762001; 294 pp
    MSC: Primary 13; 14; 32; 53; Secondary 20; 57; 65; 93;

    Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants.

    These are some of the themes of this refereed collection of papers, which grew out of the special session, “Enumerative Geometry in Physics,” held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend.

    The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.

    Readership

    Graduate students and research mathematicians interested in algebraic geometry and related disciplines.

  • Table of Contents
     
     
    • Chapter I. Enuerative or reality problems [ MR 1837106 ]
    • Sándor J. Kovács — Number of automorphisms of principally polarized abelian varieties [ MR 1837107 ]
    • Frank Sottile — Rational curves on Grassmannians: systems theory, reality, and transversality [ MR 1837108 ]
    • Alexander I. Suciu — Fundamental groups of line arrangements: enumerative aspects [ MR 1837109 ]
    • Chapter II. Variational and moduli problems [ MR 1837106 ]
    • Dan Abramovich and Aaron Bertram — The formula $12=10+2\times 1$ and its generalizations: counting rational curves on $\mathbf {F}_2$ [ MR 1837110 ]
    • Dan Abramovich and Frans Oort — Stable maps and Hurwitz schemes in mixed characteristics [ MR 1837111 ]
    • Lucia Caporaso — On modular properties of odd theta-characteristics [ MR 1837112 ]
    • Eduardo Cattani and Javier Fernandez — Asymptotic Hodge theory and quantum products [ MR 1837113 ]
    • Herbert Clemens — On rational curves in $n$-space with given normal bundle [ MR 1837114 ]
    • Ravi Vakil — A tool for stable reduction of curves on surfaces [ MR 1837115 ]
    • Chapter III. Mirror symmetry and Gromov-Witten invariants [ MR 1837106 ]
    • David A. Cox, Sheldon Katz and Yuan-Pin Lee — Virtual fundamental classes of zero loci [ MR 1837116 ]
    • Tyler J. Jarvis, Takashi Kimura and Arkady Vaintrob — Gravitational descendants and the moduli space of higher spin curves [ MR 1837117 ]
    • Bernd Kreußler — Homological mirror symmetry in dimension one [ MR 1837118 ]
    • Anvar R. Mavlyutov — The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map [ MR 1837119 ]
    • Alexander Polishchuk and Arkady Vaintrob — Algebraic construction of Witten’s top Chern class [ MR 1837120 ]
    • Alexander Postnikov — Symmetries of Gromov-Witten invariants [ MR 1837121 ]
    • Steven Rosenberg and Mihaela Vajiac — Gauge theory techniques in quantum cohomology [ MR 1837122 ]
    • C. Woodward — Gromov-Witten invariants of flag manifolds and products of conjugacy classes [ MR 1837123 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2762001; 294 pp
MSC: Primary 13; 14; 32; 53; Secondary 20; 57; 65; 93;

Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants.

These are some of the themes of this refereed collection of papers, which grew out of the special session, “Enumerative Geometry in Physics,” held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend.

The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.

Readership

Graduate students and research mathematicians interested in algebraic geometry and related disciplines.

  • Chapter I. Enuerative or reality problems [ MR 1837106 ]
  • Sándor J. Kovács — Number of automorphisms of principally polarized abelian varieties [ MR 1837107 ]
  • Frank Sottile — Rational curves on Grassmannians: systems theory, reality, and transversality [ MR 1837108 ]
  • Alexander I. Suciu — Fundamental groups of line arrangements: enumerative aspects [ MR 1837109 ]
  • Chapter II. Variational and moduli problems [ MR 1837106 ]
  • Dan Abramovich and Aaron Bertram — The formula $12=10+2\times 1$ and its generalizations: counting rational curves on $\mathbf {F}_2$ [ MR 1837110 ]
  • Dan Abramovich and Frans Oort — Stable maps and Hurwitz schemes in mixed characteristics [ MR 1837111 ]
  • Lucia Caporaso — On modular properties of odd theta-characteristics [ MR 1837112 ]
  • Eduardo Cattani and Javier Fernandez — Asymptotic Hodge theory and quantum products [ MR 1837113 ]
  • Herbert Clemens — On rational curves in $n$-space with given normal bundle [ MR 1837114 ]
  • Ravi Vakil — A tool for stable reduction of curves on surfaces [ MR 1837115 ]
  • Chapter III. Mirror symmetry and Gromov-Witten invariants [ MR 1837106 ]
  • David A. Cox, Sheldon Katz and Yuan-Pin Lee — Virtual fundamental classes of zero loci [ MR 1837116 ]
  • Tyler J. Jarvis, Takashi Kimura and Arkady Vaintrob — Gravitational descendants and the moduli space of higher spin curves [ MR 1837117 ]
  • Bernd Kreußler — Homological mirror symmetry in dimension one [ MR 1837118 ]
  • Anvar R. Mavlyutov — The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map [ MR 1837119 ]
  • Alexander Polishchuk and Arkady Vaintrob — Algebraic construction of Witten’s top Chern class [ MR 1837120 ]
  • Alexander Postnikov — Symmetries of Gromov-Witten invariants [ MR 1837121 ]
  • Steven Rosenberg and Mihaela Vajiac — Gauge theory techniques in quantum cohomology [ MR 1837122 ]
  • C. Woodward — Gromov-Witten invariants of flag manifolds and products of conjugacy classes [ MR 1837123 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.