у + Genitive + есть/нет

At an advanced level, this construction moves beyond simple physical possession to describe abstract systems, availability, and legal frameworks.

1. Syntactic Structure:

• The Possessor: Always follows the preposition у and must be in the Genitive case. Note that third-person pronouns require an н- prefix after у (у него, у неё, у них).
• The Feature (Positive): When using есть, the feature is the subject and remains in the Nominative case.
• The Feature (Negative): When using нет, which functions as the direct present-tense negative counterpart to есть (historically a contraction of 'не есть'), the feature must be in the Genitive case.

2. The Role of 'есть' and Information Structure:
In formal discourse, the inclusion of есть is a deliberate choice to assert the existence or availability of a condition or limitation as a relevant fact (the new information or rheme). If you are merely describing a known inherent quality or an attribute of something whose existence is already established, есть is typically omitted: У проекта высокий потенциал (The project has high potential) or У алгоритма строгая логика (The algorithm has strict logic). However, to state 'The system does have vulnerabilities,' you must use есть: У системы есть уязвимости (The system has vulnerabilities). Similarly, есть is used to state the existence of legal or structural elements (У компании есть права на это - The company has rights to this), but omitted when describing their attributes.

Crucially, the presence or absence of есть also distinguishes between permanent ownership or existence and temporary possession or location. For example, У меня есть паспорт means 'I own a passport' (permanent possession), whereas У меня паспорт means 'I have the passport on me right now' (temporary possession or location).

3. Past and Future Tenses:
In the past and future tenses, the verb changes. In positive statements, the verb agrees with the Nominative subject: был/была/было/были (past) or будет/будут (future). In negative statements, the past tense verb takes the invariable neuter singular form не было, while the future tense takes the third-person singular form не будет, and the feature remains in the Genitive case.

4. Formal Register vs. 'иметь':
While у + есть is common, in strict scientific, legal, or highly formal Russian, the verb иметь (to have) is actually the standard choice for attributing inherent properties, structures, or rights (e.g., система имеет структуру - the system has a structure, закон имеет силу - the law has force, иметь значение - to have significance). У + есть in formal statements often emphasizes the presence or availability of something rather than an inherent structural attribute.