πp, the value of π in `p Joseph B. Keller and Ravi Vakil The two-dimensional space `p is the set of points in the plane, with the distance between two points (x, y) and (x0 , y 0 ) defined by (|x − x0 |p + |y − y 0

Source URL: math.stanford.edu

• Integral calculus
• Length
• Mathematical analysis
• Mathematics
• Inequalities
• Ordinary differential equations
• Arc length
• Curves

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

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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

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

Journal de Théorie des Nombres de Bordeaux 00 (XXXX), 000–000 Universal covering spaces and fundamental groups in algebraic geometry as schemes par Ravi Vakil et Kirsten Wickelgren

Source URL: math.harvard.edu

• Algebraic topology
• Scheme theory
• Homotopy theory
• Algebraic geometry
• General topology
• Étale morphism
• Étale fundamental group
• Grothendieck topology
• Group scheme
• Abstract algebra
• Topology
• Algebra

INTRODUCTION TO ALGEBRAIC GEOMETRY, CLASS 12 RAVI VAKIL Contents 1. Products of projective varieties; the Segre map 1.1. P1 × P1 and the smooth quadric surface

Source URL: math.stanford.edu

• Algebraic variety
• Rational mapping
• Segre embedding
• Quasiprojective variety
• Product
• Sheaf
• Quadric
• Ample line bundle
• Proper morphism
• Geometry
• Abstract algebra
• Algebraic geometry

SPECTRAL SEQUENCES: FRIEND OR FOE? RAVI VAKIL Spectral sequences are a powerful book-keeping tool for proving things involving complicated commutative diagrams. They were introduced by Leray in the 1940’s at the same t

Source URL: math.stanford.edu

• Algebraic topology
• Spectral sequence
• Hyperhomology
• Five lemma
• Cohomology
• Clifford algebra
• Dolbeault cohomology
• Abstract algebra
• Homological algebra
• Algebra

FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASSES 43 AND 44 RAVI VAKIL C ONTENTS 1. Flat implies constant Euler characteristic

Source URL: math.stanford.edu

• Algebraic geometry
• Algebraic topology
• Homological algebra
• Projective geometry
• Vector bundles
• Flat morphism
• Sheaf
• Projective space
• Ample line bundle
• Abstract algebra
• Geometry
• Algebra