Extending Families of Curves over Log Regular Schemes by Shinichi Mochizuki Abstract: In this paper, we generalize to the “log regular case” a result of de Jong and Oort which states that any morphism (satisfying cer

Source URL: www.kurims.kyoto-u.ac.jp

• Algebraic geometry
• Morphism of algebraic varieties
• CohenMacaulay ring
• Divisor
• Blowing up
• tale morphism
• Log structure
• Smooth morphism
• Normal scheme
• Sheaf
• Toric variety
• Resolution of singularities

EQUIVARIANT ALGEBRAIC GEOMETRY JANUARY 30, 2015 Note: this was a guest lecture by Arnav Tripathy. 1. G ROTHENDIECK -R IEMANN -R OCH Let f : X → Y be a smooth proper morphism of smooth schemes

Source URL: math.stanford.edu

ON A RESULT OF ARTIN AISE JOHAN DE JONG Let k be an algebraically closed field of characteristic p > 0. Let t be a parameter and set S = Spec(k[[t]]). Let f : X → S be a smooth proper morphism with generic fibre Xη an

Source URL: math.columbia.edu

• Algebra
• Homological algebra
• Algebraic geometry
• Crystalline cohomology
• Elementary class
• Structure
• Abstract algebra
• Model theory
• Mathematics

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