A DESCRIPTION OF THE OUTER AUTOMORPHISM OF S6, AND THE INVARIANTS OF SIX POINTS IN PROJECTIVE SPACE BEN HOWARD, JOHN MILLSON, ANDREW SNOWDEN, AND RAVI VAKIL A BSTRACT. We use a simple description of the outer automorphis

Source URL: math.stanford.edu

• Lie groups
• Symmetry
• Algebraic groups
• Automorphism
• Outer automorphism group
• E6
• Inner automorphism
• Out
• Moduli space
• Abstract algebra
• Algebra
• Group theory

THE AFFINE STRATIFICATION NUMBER AND THE MODULI SPACE OF CURVES MIKE ROTH AND RAVI VAKIL A BSTRACT. We define the affine stratification number asn X of a scheme X. For X equidimensional, it is the minimal number k such t

Source URL: math.stanford.edu

• Algebraic space
• Flat morphism
• Blowing up
• Affine geometry
• Proj construction
• Codimension
• Affine connection
• Algebraic variety
• Geometry
• Abstract algebra
• Algebraic geometry

RELATIVE VIRTUAL LOCALIZATION AND VANISHING OF TAUTOLOGICAL CLASSES ON MODULI SPACES OF CURVES TOM GRABER AND RAVI VAKIL A BSTRACT. We prove a localization formula for the moduli space of stable relative maps. As an appl

Source URL: math.stanford.edu

• Moduli theory
• Algebraic topology
• String theory
• Invariant theory
• Moduli space
• Gromov–Witten invariant
• Moduli of algebraic curves
• ELSV formula
• Stable map
• Abstract algebra
• Algebraic geometry
• Algebra

COMPACTIFICATION OF THE UNIVERSAL PICARD OVER THE MODULI OF STABLE CURVES TYLER J. JARVIS A. This article provides two different, but closely related, moduli problems, which in characteristic zero pr

Source URL: math.byu.edu

• Moduli space
• Algebraic stack
• Ample line bundle
• Sheaf
• Compactification
• Modular curve
• Proper morphism
• Torsion tensor
• Algebraic space
• Abstract algebra
• Geometry
• Algebraic geometry

A TOOL FOR STABLE REDUCTION OF CURVES ON SURFACES RAVI VAKIL Abstract. In the study of the geometry of curves on surfaces, the following question often arises: given a one-parameter family of divisors over a pointed

Source URL: math.stanford.edu

• Moduli theory
• Vector bundles
• Analytic number theory
• Elliptic curve
• Group theory
• Intersection number
• Curve
• Divisor
• Moduli space
• Abstract algebra
• Geometry
• Algebraic geometry

THE ENUMERATIVE GEOMETRY OF RATIONAL AND ELLIPTIC CURVES IN PROJECTIVE SPACE RAVI VAKIL Abstract. We study the geometry of moduli spaces of genus 0 and 1 curves in Pn with specified contact with a hyperplane H. We comput

Source URL: math.stanford.edu

THE EQUATIONS FOR THE MODULI SPACE OF n POINTS ON THE LINE BENJAMIN HOWARD, JOHN MILLSON, ANDREW SNOWDEN AND RAVI VAKIL A BSTRACT. A central question in invariant theory is that of determining the relations among invaria

Source URL: math.stanford.edu

• Topological graph theory
• Graph coloring
• Graph structure theorem
• Graph theory
• Mathematics
• Graph

Proceedings of 7th G¨ okova Geometry-Topology Conference, pp, 1 – 7 On the tautological ring of Mg,n

Source URL: math.stanford.edu

• Moduli theory
• Algebraic curves
• Invariant theory
• Moduli space
• ELSV formula
• Moduli of algebraic curves
• Hyperelliptic curve
• Elliptic curve
• Chow ring
• Algebraic geometry
• Abstract algebra
• Geometry

A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into Pn Ravi Vakil∗ and Aleksey Zinger† September 7, 2007 Abstract

Source URL: math.stanford.edu

• Moduli theory
• Differential topology
• String theory
• Symplectic topology
• Moduli space
• Blowing up
• Resolution of singularities
• Orbifold
• Stable map
• Abstract algebra
• Algebraic geometry
• Geometry

THE MODULI SPACE OF CURVES AND ITS TAUTOLOGICAL RING RAVI VAKIL The moduli space of curves has proven itself a central object in geometry. The past decade has seen substantial progress in understanding the moduli space o

Source URL: math.stanford.edu

• Moduli theory
• Algebraic geometry
• Invariant theory
• Vector bundles
• Moduli space
• Projective geometry
• Moduli of algebraic curves
• Line bundle
• Algebraic stack
• Abstract algebra
• Geometry
• Topology