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I am studying theoretical physics. Currently I feel need for getting some understanding of algebraic geometry and Calabi-Yau manifolds (knowing almost nothing about either algebraic geometry and commutative algebra or complex geometry, though having studied a lot of general relativity, hence Riemannian geometry, and some symplectic geometry through Hamiltonian mechanics).

I remember reading some very clearly written books, which helped me getting into subjects (such as Seifert and Threlfall's "Topology", Milnor's books, Arnold's "ODE", "Modern Geometric Structures and Fields" by Novikov and Taimanov). Could you recommend me books with that kind of teaching material, which both is clear and treats quite big parts of the subjects i want to study? It will be especially good if there is one with some examples from physics.

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  • $\begingroup$ What areas of theoretical physics do you want to go into? Most physicists work with complex manifolds, rather than with algebraic varieties, so if you want to understand 95% of the literature, it might be best to start with complex geometry. Have you looked at these Cambridge Part III notes: caramdir.at/uploads/math/piii-cm/complex-manifolds.pdf? $\endgroup$
    – Kenny Wong
    Commented Jun 23, 2017 at 10:25
  • $\begingroup$ Maybe you're interested in gauged linear sigma models? If so, then check out the physics parts of the Mirror Symmetry book claymath.org/library/monographs/cmim01c.pdf $\endgroup$
    – Kenny Wong
    Commented Jun 23, 2017 at 10:27
  • $\begingroup$ @KennyWong i want to fully understand this one Mirror Symmetry book, actually, and to work in string theory. And the reason i am asking for reference is because of the math preliminaries part has seemed to be extremely short. No, i have not look at these notes. Thank you for your suggestion! $\endgroup$
    – user108687
    Commented Jun 23, 2017 at 11:10
  • $\begingroup$ You could also look at Griffths & Harris, Chapter 0. $\endgroup$
    – Kenny Wong
    Commented Jun 23, 2017 at 12:10
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    $\begingroup$ And by the way, Mark Gross' contribution to "Calabi-Yau manifolds and related geometries" might be useful. $\endgroup$
    – Kenny Wong
    Commented Jun 23, 2017 at 12:18

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