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Ravi Vakil
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21	RECURSIONS FOR CHARACTERISTIC NUMBERS OF GENUS ONE PLANE CURVES RAVI VAKIL Abstract. Characteristic numbers of families of maps of nodal curves to P2 are dened as Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2002-02-22 23:12:01 Differential geometry Intersection theory Vector bundles Divisor Dual curve Linear system of divisors Ample line bundle Chow ring Curve Geometry Abstract algebra Algebraic geometry
22	THE MODULI SPACE OF CURVES AND GROMOV-WITTEN THEORY RAVI VAKIL A BSTRACT. The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2006-05-26 15:48:29 Moduli theory Algebraic curves Invariant theory Complex manifolds Moduli space Moduli of algebraic curves Riemann–Roch theorem Ample line bundle Divisor Algebraic geometry Abstract algebra Geometry
23	ABSOLUTE GALOIS ACTS FAITHFULLY ON THE COMPONENTS OF THE MODULI SPACE OF SURFACES: A BELYI-TYPE THEOREM IN HIGHER DIMENSION ROBERT W. EASTON AND RAVI VAKIL A BSTRACT. Given an object over Q, there is often no reason for Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2007-07-31 17:36:23 Birational geometry Moduli theory Absolute Galois group Enriques–Kodaira classification Moduli space XTR Étale cohomology Abstract algebra Algebra Galois theory
24	Proceedings of Symposia in Pure Mathematics Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus Izzet Coskun and Ravi Vakil Abstract. We describe recent work on positive descri Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2008-09-23 16:57:18 Algebraic geometry Representation theory Algebraic combinatorics Projective geometry Differential geometry Grassmannian Schubert variety Littlewood–Richardson rule Projective space Abstract algebra Algebra Mathematics
25	GENUS 0 AND 1 HURWITZ NUMBERS: RECURSIONS, FORMULAS, AND GRAPH-THEORETIC INTERPRETATIONS RAVI VAKIL Abstract. We derive a closed-form expression for all genus 1 Hurwitz numbers, and give a simple new graph-theoretic inte Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2002-02-22 23:12:01 Branch point Complex analysis Riemann–Hurwitz formula Mathematical analysis Abstract algebra Mathematics
26	MURPHY’S LAW IN ALGEBRAIC GEOMETRY: BADLY-BEHAVED DEFORMATION SPACES RAVI VAKIL A BSTRACT. We consider the question: “How bad can the deformation space of an object be?” The answer seems to be: “Unless there is s Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2005-07-07 21:44:12 Moduli theory Scheme theory Invariant theory Algebraic surfaces Moduli space Resolution of singularities Enriques–Kodaira classification Surface of general type Moduli of algebraic curves Algebraic geometry Geometry Abstract algebra
27	COUNTING CURVES ON RATIONAL SURFACES RAVI VAKIL Abstract. In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2002-02-22 23:11:59 String theory Symplectic topology Complex manifolds Algebraic topology Stable map Gromov–Witten invariant Differential geometry of surfaces Riemann–Hurwitz formula Canonical bundle Algebraic geometry Geometry Abstract algebra
28	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 Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2008-01-23 14:21:23 Lie groups Symmetry Algebraic groups Automorphism Outer automorphism group E6 Inner automorphism Out Moduli space Abstract algebra Algebra Group theory
29	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 Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2004-06-22 14:24:22 Algebraic space Flat morphism Blowing up Affine geometry Proj construction Codimension Affine connection Algebraic variety Geometry Abstract algebra Algebraic geometry
30	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 Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2004-12-20 16:33:15 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

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