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Topics in algebraic geometry

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arxiv 1104.5035 v1 pith:II74O7LS submitted 2011-04-26 math.AG

Caucher Birkar This is my paper · ORCID
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Lecture notes of an algebraic geometry graduate course. The topics covered are as follows. Cohomology: ext sheaves and groups, cohomology with support, local cohomology, local duality. Duality: relative duality, Cohen-Macaulay schemes. Morphisms of schemes: flatness and base change and related topics. Hilbert and Quotient schemes.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Geometric Syzygy Conjecture in Positive Characteristic

    math.AG 2025-08 conditional novelty 7.0 of 10

    The Geometric Syzygy Conjecture holds for general canonical curves over algebraically closed fields of characteristic at least 2g-4.

  2. From Hitchin Systems to Rational Elliptic Surfaces with C*-actions via Orbifold Hilbert Schemes

    math.AG 2025-09 conditional novelty 6.0 of 10

    Compactifying certain Hitchin systems via orbifold Hilbert schemes yields four rational elliptic surfaces, all obtained by blowing up the second Hirzebruch surface.

  3. On supported deformations and birational isotriviality

    math.AG 2025-06 conditional novelty 6.0 of 10

    For semistable fibrations with general type fibers, a Kodaira-Spencer class supported on a suitable non-movable, foliation-invariant divisor forces the general fibers to be birational.

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