Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hodge Theory and Deformations of Affine Cones of Subcanonical Projective
  Varieties   We investigate the relation between the Hodge theory of a smooth subcanonical
$n$-dimensional projective variety $X$ and the deformation theory of the affine
cone $A_X$ over $X$. We start by identifying $H^{n-1,1}_{\mathrm{prim}}(X)$ as
a distinguished graded component of the module of first order deformations of
$A_X$, and later on we show how to identify the whole primitive cohomology of
$X$ as a distinguished graded component of the Hochschild cohomology module of
the punctured affine cone over $X$. In the particular case of a projective
smooth hypersurface $X$ we recover Griffiths' isomorphism between the primitive
cohomology of $X$ and certain distinguished graded components of the Milnor
algebra of a polynomial defining $X$. The main result of the article can be
effectively exploited to compute Hodge numbers of smooth subcanonical
projective varieties. We provide a few example computation, as well a SINGULAR
code, for Fano and Calabi-Yau threefolds.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ
30
The categories of this paper are: q-alg