Classical Algebraic Geometry: A Modern View

By Igor Dolgachev. 2012

748 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/8e6acc389a78eeb984f2a1da5aafbd82da2eb109

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. C. Lehn
2. Christoph Sorger
3. Duco van Straten
4. Hao Yang
5. Yang Guo
6. M. Lehn
7. Chen Lan
8. Y. Miao

In Geometry and Topology

1. Caterina Stoppato
2. A. Verra
3. Serge Cantat
4. Min-xin Huang
5. G. Farkas
6. Graziano Gentili
7. Christoph Sorger
8. M. Lehn

In Theoretical Computer Science

1. C. Lehn
2. Christoph Sorger
3. Duco van Straten
4. Hao Yang
5. Yang Guo
6. M. Lehn
7. Chen Lan
8. Y. Miao

Citations in the corpus

• Twistor transforms of quaternionic functions and orthogonal complex structures (2012, background): “It is one of a number of quartic scrolls whose classification (described in [9] and references therein) might be relevant for the treatment of analogous orthogonal complex structures.”
• Twisted cubics on cubic fourfolds (2013, methodology): “We refer to the book of Dolgachev [11] for further information.”
• Regular Black Holes: A Short Topic Review (2023, methodology): “Segré notation (or Segré symbol) is a systematic method for studying the complete intersection of two quadrics in algebraic geometry [219].”
• The geometry of the moduli space of odd spin curves (2010, background): “Even though the geometry and the intricate combinatorics of θ(C) have been studied classically, see [Dol12], [DK93] for a modern account, it has only been recently proved in [CS03] that one can reconstruct a general curve [C] ∈Mg from the hyperplane configuration θ(C).”
• Rational surfaces with a large group of automorphisms (2011, background): “It is classically known that a surface of degree 4 in P(4) that spans P(4) is either an anticanonical del Pezzo surface, or a cone over an elliptic curve, or a projection of a surface of degree 4 in P(5) (see [34, 35] and [18]).”
• Flexibility of affine cones over del Pezzo surfaces of degree 4 and 5 (2011, neutral): “Functional Analysis and Its Applications, Springer Verlag, 2013, 47 (4), pp.”
• Refined stable pair invariants for E-, M- and [p, q]-strings (2013, background): “the degree six A1 ×A2 del Pezzo is a determinantal variety in P6 and the degree five A4 del Pezzo is given by five linear quadrics in P5 [20].”