= Ravi Vakil
{c}
<Ravi Vakil> works on <algebraic geometry>. His Stanford page identifies the specialization and his exposition <The Rising Sea: Foundations of Algebraic Geometry by Ravi Vakil (2017 draft)>.https://math.stanford.edu/~vakil/[Author research and book page]{ref}
The book builds the geometry of polynomial equations through <schemes>, beginning with affine constructions and developing local-to-global methods. A <rational map> may be defined only on a dense open set; a <birational morphism> can change a geometric model while preserving its <function field>. These distinctions connect concrete equations with the abstract language needed to compare algebraic spaces.<The Rising Sea: Foundations of Algebraic Geometry by Ravi Vakil (2017 draft)>[Section 0.4, chapter 3 and rational-map development]{ref}
\Image[https://math.stanford.edu/~vakil/Vakil_R-3.jpg]
{title=Ravi Vakil}
{description=Portrait linked from Ravi Vakil’s official Stanford homepage.}
{source=https://math.stanford.edu/~vakil/}
{width=220}
Back to article page
