Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Infinitesimal Torelli theorem for regular surfaces with very
  ample canonical divisor   Let $X$ be a smooth compact complex surface subject to the following
conditions:
  (i) the canonical line bundle $\mathcal{O}_X(K_X) $ is very ample,
  (ii) the irregularity $q(X): = h^1(\mathcal{O}_X) =0$,
  (iii) $X$ contains no rational normal curves of degree $\leq (p_g-1)$,
  (iv) the multiplication map $m_2: Sym^2(H^0(\mathcal{O}_X(K_X)))
\longrightarrow H^0 (\mathcal{O}_X (2K_X))$ is surjective.
  It is shown that the Infinitesimal Torelli holds for such $X$.
  Our proof is based on the study of the cup-product
  $$ H^1 (\Theta_X) \longrightarrow (\mathcal{O}_X(K_X))^{\ast} \otimes H^1
(\Omega_X) $$ where $\Theta_X$ (resp. $\Omega_X$) is the holomorphic tangent
(resp. cotangent) bundle of $X$. Conceptually, the approach consists of lifting
the data of the cohomological cup-product above to the category of complexes of
coherent sheaves of $X$. This establishes connections between the geometry of
the canonical map and the above cup-product by exhibiting geometrically
meaningful objects in the category of (short) exact complexes of coherent
sheaves on $X$.

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The categories of this paper are: hep-th
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The categories of this paper are: physics
11
The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: q-alg