Algebraic geometry
Graduate · Math
Syllabus focus
Theoretical / proof-based
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$1,162 · Algebraic geometry · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.
Topics typically covered
Theoretical / proof-based
Varieties and morphisms
- Affine and projective varieties; Nullstellensatz
- Regular maps, rational maps, and birational equivalence
- Dimension, tangent spaces, and smoothness
- Bezout's theorem and intersection multiplicity (introduction)
- Blow-ups and resolution of singularities (overview)
Schemes and sheaves
- Sheaves on topological spaces; sheafification
- Affine schemes and Spec of a ring
- Schemes: gluing, morphisms, and closed subschemes
- Structure sheaf and locally ringed spaces
- Fiber products and base change (introduction)
Cohomology and curves
- Sheaf cohomology on schemes (Cech and derived functors overview)
- Divisors and line bundles on curves
- Riemann–Roch theorem for curves
- Genus and classification of algebraic curves (introduction)
- Moduli of elliptic curves (preview)
Notes
Topics reflect common graduate algebraic geometry syllabi at US universities. A full year typically moves from classical varieties toward scheme-theoretic foundations and cohomological tools.